48, Solutions to Red Wins in, 3, moves in Connect Four ------------------------------------------------ Detailed Solution to problem number, 1 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 0, 0, 1, 0, 0 2, 1, 1, 1, 2, 2, 2 1, 2, 2, 1, 1, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 0, 1, 1, 0, 0 2, 1, 1, 1, 2, 2, 2 1, 2, 2, 1, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 2, 0, 0 0, 0, 0, 1, 1, 0, 0 2, 1, 1, 1, 2, 2, 2 1, 2, 2, 1, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 2, 0, 0 0, 0, 1, 1, 1, 0, 0 2, 1, 1, 1, 2, 2, 2 1, 2, 2, 1, 1, 2, 1 This is double-or-nothing in columns, 2, 6 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 2, 0, 0 0, 0, 0, 1, 1, 1, 0 2, 1, 1, 1, 2, 2, 2 1, 2, 2, 1, 1, 2, 1 This is double-or-nothing in columns, 3, 7 ------------------------------------------------ Detailed Solution to problem number, 2 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 1, 0, 1, 1 2, 2, 1, 2, 0, 1, 1 2, 1, 2, 1, 0, 2, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 7 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 2, 0, 1, 0, 1, 1 2, 2, 1, 2, 0, 1, 1 2, 1, 2, 1, 0, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 7 If Black goes in column, 7, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 0, 0, 0, 0, 0, 0, 1 0, 2, 0, 1, 0, 1, 1 2, 2, 1, 2, 0, 1, 1 2, 1, 2, 1, 0, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 0, 0, 0, 0, 0, 0, 1 0, 2, 0, 1, 0, 1, 1 2, 2, 1, 2, 0, 1, 1 2, 1, 2, 1, 1, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 0, 0, 0, 0, 0, 0, 1 0, 2, 0, 1, 0, 1, 1 2, 2, 1, 2, 2, 1, 1 2, 1, 2, 1, 1, 2, 2 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 0, 0, 0, 0, 0, 0, 1 0, 2, 0, 1, 1, 1, 1 2, 2, 1, 2, 2, 1, 1 2, 1, 2, 1, 1, 2, 2 ------------------------------------------------ Detailed Solution to problem number, 3 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 0, 1, 0, 1 2, 1, 2, 0, 2, 1, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 0, 2, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 1, 2, 3, 4, 5, 6, 7 If Black goes in column, 1, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 0, 2, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 2, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 2, 0, 0, 0, 0 1, 1, 1, 1, 2, 0, 0 1, 2, 2, 2, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 If Black goes in column, 2, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 0, 2, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 2, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 1, 1, 1, 1, 2, 0, 0 1, 2, 2, 2, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 0, 2, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 2, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 1, 2, 0, 0 1, 2, 2, 2, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 2, 2, 1, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 1, 1, 1, 1 2, 1, 2, 2, 2, 1, 2 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 2, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 0, 2, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 2, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 2, 0, 0 1, 1, 1, 0, 2, 0, 0 1, 2, 2, 2, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 2, 0, 0 1, 1, 1, 1, 2, 0, 0 1, 2, 2, 2, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 2, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 0, 2, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 2, 0 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 2, 0 1, 2, 2, 2, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 If Black goes in column, 7, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 2 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 0, 2, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 2 1, 2, 2, 0, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 2, 0, 2 1, 2, 2, 2, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 1, 2, 0, 2 1, 2, 2, 2, 1, 1, 1 2, 1, 2, 1, 2, 1, 2 ------------------------------------------------ Detailed Solution to problem number, 4 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 0, 0, 0, 0, 0, 1, 0 2, 2, 2, 1, 1, 1, 2 2, 1, 1, 1, 2, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 7 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 0, 0, 0, 0, 0, 1, 1 2, 2, 2, 1, 1, 1, 2 2, 1, 1, 1, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 7 If Black goes in column, 7, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 2 0, 0, 0, 0, 0, 1, 1 2, 2, 2, 1, 1, 1, 2 2, 1, 1, 1, 2, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 2 0, 0, 0, 1, 0, 1, 1 2, 2, 2, 1, 1, 1, 2 2, 1, 1, 1, 2, 2, 1 This is double-or-nothing in columns, 4, 5 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 2 0, 0, 0, 0, 1, 1, 1 2, 2, 2, 1, 1, 1, 2 2, 1, 1, 1, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 2 0, 0, 0, 2, 1, 1, 1 2, 2, 2, 1, 1, 1, 2 2, 1, 1, 1, 2, 2, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 1, 0, 2, 2 0, 0, 0, 2, 1, 1, 1 2, 2, 2, 1, 1, 1, 2 2, 1, 1, 1, 2, 2, 1 ------------------------------------------------ Detailed Solution to problem number, 5 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 1, 0, 1, 0, 2, 0 1, 2, 0, 2, 0, 2, 0 1, 1, 0, 1, 0, 1, 0 2, 2, 0, 1, 0, 2, 0 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 1, 0, 1, 0, 2, 0 1, 2, 0, 2, 0, 2, 0 1, 1, 0, 1, 0, 1, 0 2, 2, 1, 1, 0, 2, 0 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 1, 0, 1, 0, 2, 0 1, 2, 0, 2, 0, 2, 0 1, 1, 2, 1, 0, 1, 0 2, 2, 1, 1, 0, 2, 0 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 1, 0, 1, 0, 2, 0 1, 2, 1, 2, 0, 2, 0 1, 1, 2, 1, 0, 1, 0 2, 2, 1, 1, 0, 2, 0 This is double-or-nothing in columns, 1, 5 ------------------------------------------------ Detailed Solution to problem number, 6 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 0, 0, 0, 1, 0, 1, 2 1, 0, 1, 1, 2, 1, 1 2, 0, 2, 2, 1, 2, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 0, 0, 0, 1, 0, 1, 2 1, 0, 1, 1, 2, 1, 1 2, 1, 2, 2, 1, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 2 If Black goes in column, 2, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 0, 0, 0, 1, 0, 1, 2 1, 2, 1, 1, 2, 1, 1 2, 1, 2, 2, 1, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 0, 0, 1, 1, 0, 1, 2 1, 2, 1, 1, 2, 1, 1 2, 1, 2, 2, 1, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 0, 0, 1, 1, 2, 1, 2 1, 2, 1, 1, 2, 1, 1 2, 1, 2, 2, 1, 2, 2 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 1, 0, 0 0, 0, 1, 1, 2, 1, 2 1, 2, 1, 1, 2, 1, 1 2, 1, 2, 2, 1, 2, 2 ------------------------------------------------ Detailed Solution to problem number, 7 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 2, 1, 1, 0, 0, 0, 0 2, 2, 1, 1, 0, 0, 0 1, 2, 1, 2, 2, 1, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 2, 1, 1, 0, 0, 0, 0 2, 2, 1, 1, 0, 1, 0 1, 2, 1, 2, 2, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 2, 1, 1, 0, 0, 0, 0 2, 2, 1, 1, 2, 1, 0 1, 2, 1, 2, 2, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 2, 1, 1, 0, 1, 0, 0 2, 2, 1, 1, 2, 1, 0 1, 2, 1, 2, 2, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 2, 1, 1, 2, 1, 0, 0 2, 2, 1, 1, 2, 1, 0 1, 2, 1, 2, 2, 1, 1 ------------------------------------------------ Detailed Solution to problem number, 8 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 2, 0 0, 1, 0, 0, 0, 1, 0 0, 2, 1, 2, 1, 2, 2 0, 1, 2, 2, 1, 1, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 2, 0 0, 1, 0, 0, 1, 1, 0 0, 2, 1, 2, 1, 2, 2 0, 1, 2, 2, 1, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 2, 2, 0 0, 1, 0, 0, 1, 1, 0 0, 2, 1, 2, 1, 2, 2 0, 1, 2, 2, 1, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 2, 2, 0 0, 1, 0, 1, 1, 1, 0 0, 2, 1, 2, 1, 2, 2 0, 1, 2, 2, 1, 1, 2 This is double-or-nothing in columns, 3, 7 ------------------------------------------------ Detailed Solution to problem number, 9 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 2, 0, 0, 0 2, 0, 1, 1, 0, 0, 0 2, 0, 2, 2, 0, 2, 2 1, 0, 1, 2, 1, 1, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 2, 0, 0, 0 2, 0, 1, 1, 0, 0, 0 2, 0, 2, 2, 1, 2, 2 1, 0, 1, 2, 1, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 2, 0, 0, 0 2, 0, 1, 1, 0, 0, 0 2, 0, 2, 2, 1, 2, 2 1, 0, 1, 2, 1, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 2, 0, 0, 0 2, 0, 1, 1, 1, 0, 0 2, 0, 2, 2, 1, 2, 2 1, 0, 1, 2, 1, 1, 1 This is double-or-nothing in columns, 5, 6 ------------------------------------------------ Detailed Solution to problem number, 10 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 1, 0, 0 0, 2, 0, 0, 1, 0, 0 0, 1, 2, 1, 2, 1, 2 0, 1, 2, 2, 1, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 1, 0, 0 0, 2, 0, 1, 1, 0, 0 0, 1, 2, 1, 2, 1, 2 0, 1, 2, 2, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 2, 1, 0, 0 0, 2, 0, 1, 1, 0, 0 0, 1, 2, 1, 2, 1, 2 0, 1, 2, 2, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 2, 1, 0, 0 0, 2, 0, 1, 1, 1, 0 0, 1, 2, 1, 2, 1, 2 0, 1, 2, 2, 1, 2, 1 This is double-or-nothing in columns, 3, 7 ------------------------------------------------ Detailed Solution to problem number, 11 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 1, 0, 2, 0, 0 2, 0, 2, 0, 2, 0, 2 1, 0, 2, 0, 1, 0, 1 1, 2, 2, 0, 1, 0, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 1, 0, 2, 0, 0 2, 0, 2, 0, 2, 0, 2 1, 0, 2, 0, 1, 0, 1 1, 2, 2, 0, 1, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 1, 0, 2, 0, 0 2, 0, 2, 0, 2, 0, 2 1, 0, 2, 0, 1, 0, 1 1, 2, 2, 2, 1, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 1, 0, 2, 0, 0 2, 0, 2, 0, 2, 0, 2 1, 0, 2, 0, 1, 1, 1 1, 2, 2, 2, 1, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 1, 0, 2, 0, 0 2, 0, 2, 0, 2, 0, 2 1, 0, 2, 2, 1, 1, 1 1, 2, 2, 2, 1, 1, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 1, 0, 2, 0, 0 2, 0, 2, 1, 2, 0, 2 1, 0, 2, 2, 1, 1, 1 1, 2, 2, 2, 1, 1, 1 ------------------------------------------------ Detailed Solution to problem number, 12 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 1, 0 1, 1, 1, 2, 2, 1, 2 1, 2, 1, 2, 1, 2, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 1, 0, 0, 1, 0 1, 1, 1, 2, 2, 1, 2 1, 2, 1, 2, 1, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 2, 1, 0, 0, 1, 0 1, 1, 1, 2, 2, 1, 2 1, 2, 1, 2, 1, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 2, 1, 1, 0, 1, 0 1, 1, 1, 2, 2, 1, 2 1, 2, 1, 2, 1, 2, 2 This is double-or-nothing in columns, 4, 5 ------------------------------------------------ Detailed Solution to problem number, 13 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 1, 0, 2, 1 1, 2, 0, 2, 0, 1, 2 2, 1, 2, 1, 2, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 1 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 0, 0, 0, 0 1, 0, 0, 1, 0, 2, 1 1, 2, 0, 2, 0, 1, 2 2, 1, 2, 1, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 1 If Black goes in column, 1, then the position is 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 0, 0, 0, 0, 0, 0 1, 0, 0, 1, 0, 2, 1 1, 2, 0, 2, 0, 1, 2 2, 1, 2, 1, 2, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 0, 0, 0, 0, 0, 0 1, 1, 0, 1, 0, 2, 1 1, 2, 0, 2, 0, 1, 2 2, 1, 2, 1, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 0, 0, 0, 0, 0, 0 1, 1, 0, 1, 0, 2, 1 1, 2, 2, 2, 0, 1, 2 2, 1, 2, 1, 2, 2, 1 ------------------------------------------------ Detailed Solution to problem number, 14 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 0, 0 0, 0, 0, 0, 1, 0, 0 2, 1, 2, 1, 2, 2, 1 1, 2, 2, 1, 1, 2, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 0, 0 0, 0, 0, 1, 1, 0, 0 2, 1, 2, 1, 2, 2, 1 1, 2, 2, 1, 1, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 1, 0, 0 0, 0, 0, 1, 1, 0, 0 2, 1, 2, 1, 2, 2, 1 1, 2, 2, 1, 1, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 1, 0, 0 0, 0, 1, 1, 1, 0, 0 2, 1, 2, 1, 2, 2, 1 1, 2, 2, 1, 1, 2, 2 This is double-or-nothing in columns, 2, 6 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 1, 0, 0 0, 0, 0, 1, 1, 1, 0 2, 1, 2, 1, 2, 2, 1 1, 2, 2, 1, 1, 2, 2 This is double-or-nothing in columns, 3, 4, 7 ------------------------------------------------ Detailed Solution to problem number, 15 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 0, 0 2, 2, 1, 2, 1, 1, 2 1, 1, 1, 2, 2, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 0, 0 0, 1, 1, 0, 0, 0, 0 2, 2, 1, 2, 1, 1, 2 1, 1, 1, 2, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 0, 1, 1, 0, 0, 0, 0 2, 2, 1, 2, 1, 1, 2 1, 1, 1, 2, 2, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 0, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 1, 1, 2 1, 1, 1, 2, 2, 2, 1 This is double-or-nothing in columns, 1, 5 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 0, 1, 1, 0, 1, 0, 0 2, 2, 1, 2, 1, 1, 2 1, 1, 1, 2, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 0, 1, 1, 2, 1, 0, 0 2, 2, 1, 2, 1, 1, 2 1, 1, 1, 2, 2, 2, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 1, 0, 0, 0 0, 1, 1, 2, 1, 0, 0 2, 2, 1, 2, 1, 1, 2 1, 1, 1, 2, 2, 2, 1 ------------------------------------------------ Detailed Solution to problem number, 16 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 0, 0, 0, 1, 1, 1, 2 1, 0, 0, 2, 2, 2, 1 2, 0, 2, 1, 2, 1, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 0, 0, 0, 1, 1, 1, 2 1, 0, 1, 2, 2, 2, 1 2, 0, 2, 1, 2, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 0, 0, 2, 1, 1, 1, 2 1, 0, 1, 2, 2, 2, 1 2, 0, 2, 1, 2, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 1, 0, 0 0, 0, 2, 1, 1, 1, 2 1, 0, 1, 2, 2, 2, 1 2, 0, 2, 1, 2, 1, 1 This is double-or-nothing in columns, 2, 4 ------------------------------------------------ Detailed Solution to problem number, 17 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 1, 0, 2, 0 2, 1, 0, 2, 1, 2, 1 2, 2, 1, 2, 1, 1, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 1, 1, 2, 0 2, 1, 0, 2, 1, 2, 1 2, 2, 1, 2, 1, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 1, 0, 1, 1, 2, 0 2, 1, 0, 2, 1, 2, 1 2, 2, 1, 2, 1, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 1, 0, 1, 1, 2, 0 2, 1, 1, 2, 1, 2, 1 2, 2, 1, 2, 1, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 1, 2, 1, 1, 2, 0 2, 1, 1, 2, 1, 2, 1 2, 2, 1, 2, 1, 1, 2 Red can win immediately by moving in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 2, 0, 0 0, 1, 2, 1, 1, 2, 0 2, 1, 1, 2, 1, 2, 1 2, 2, 1, 2, 1, 1, 2 ------------------------------------------------ Detailed Solution to problem number, 18 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 0, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 0, 1, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 0, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 1, 2, 3, 4, 5, 6, 7 If Black goes in column, 1, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 0, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 2, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 1, 1, 0 2, 2, 0, 1, 2, 2, 0 1, 1, 1, 2, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 If Black goes in column, 2, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 0, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 2, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 1, 1, 0 2, 2, 0, 1, 2, 2, 0 1, 1, 1, 2, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 2, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 0, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 2, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 2, 0, 2, 2, 0 1, 1, 1, 2, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 2, 1, 2, 2, 0 1, 1, 1, 2, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 2, 1, 2, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 1, 1, 2, 0 2, 1, 2, 2, 1, 2, 1 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 0, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 2, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 1, 2, 2, 0 1, 1, 1, 2, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 0, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 2, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 1, 2, 2, 0 1, 1, 1, 2, 1, 2, 0 2, 1, 2, 1, 1, 2, 1 If Black goes in column, 7, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 2 2, 1, 2, 0, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 0, 1, 2, 2 2, 1, 2, 1, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 0, 2, 2, 0 1, 1, 1, 2, 1, 2, 2 2, 1, 2, 1, 1, 2, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 2, 2, 0, 1, 2, 2, 0 1, 1, 1, 2, 1, 2, 2 2, 1, 2, 1, 1, 2, 1 ------------------------------------------------ Detailed Solution to problem number, 19 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 0, 0, 1, 1 1, 2, 1, 0, 0, 2, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 0, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 1, 2, 3, 4, 5, 6, 7 If Black goes in column, 1, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 0, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 2, 0, 0, 0, 0 1, 1, 1, 2, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 2, 1, 0, 0, 0 1, 1, 1, 2, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 If Black goes in column, 2, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 0, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 1, 1, 1, 2, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 1, 0, 0, 0 1, 1, 1, 2, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 0, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 2, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 0, 2, 1, 0, 0, 0 1, 1, 1, 2, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 2, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 1, 0, 2, 2 2, 1, 2, 2, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 0, 0, 1, 1 1, 2, 1, 1, 2, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 2, 2, 2 This is double-or-nothing in columns, 4, 5 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 0, 1, 1, 1 1, 2, 1, 1, 2, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 2, 1, 1, 1 1, 2, 1, 1, 2, 2, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 1, 1, 1, 0, 2, 2 2, 1, 2, 2, 1, 1, 1 1, 2, 1, 1, 2, 2, 2 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 2, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 0, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 2, 0 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 2, 0 1, 1, 1, 2, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 1, 0, 2, 0 1, 1, 1, 2, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 If Black goes in column, 7, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 2 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 0, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 2 1, 1, 1, 0, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 2 1, 1, 1, 2, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 1, 0, 0, 2 1, 1, 1, 2, 0, 2, 2 2, 1, 2, 1, 0, 1, 1 1, 2, 1, 1, 0, 2, 2 ------------------------------------------------ Detailed Solution to problem number, 20 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 2, 0, 0 0, 1, 0, 0, 1, 0, 0 0, 1, 0, 2, 1, 1, 2 1, 2, 2, 1, 2, 1, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 2, 0, 0 0, 1, 0, 0, 1, 1, 0 0, 1, 0, 2, 1, 1, 2 1, 2, 2, 1, 2, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 6 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 2, 2, 0 0, 1, 0, 0, 1, 1, 0 0, 1, 0, 2, 1, 1, 2 1, 2, 2, 1, 2, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 2, 2, 0 0, 1, 0, 1, 1, 1, 0 0, 1, 0, 2, 1, 1, 2 1, 2, 2, 1, 2, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 7 If Black goes in column, 7, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 2, 2, 0 0, 1, 0, 1, 1, 1, 2 0, 1, 0, 2, 1, 1, 2 1, 2, 2, 1, 2, 1, 2 Red can win immediately by moving in column, 7 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 2, 2, 1 0, 1, 0, 1, 1, 1, 2 0, 1, 0, 2, 1, 1, 2 1, 2, 2, 1, 2, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 7 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 2, 2, 0 0, 1, 0, 0, 1, 1, 1 0, 1, 0, 2, 1, 1, 2 1, 2, 2, 1, 2, 1, 2 This is double-or-nothing in columns, 4, 7 ------------------------------------------------ Detailed Solution to problem number, 21 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 2, 2, 0, 0, 1, 1, 1 2, 1, 0, 0, 2, 2, 1 1, 1, 0, 0, 2, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 2, 2, 0, 0, 1, 1, 1 2, 1, 0, 0, 2, 2, 1 1, 1, 1, 0, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 2, 2, 0, 0, 1, 1, 1 2, 1, 0, 0, 2, 2, 1 1, 1, 1, 2, 2, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 2, 2, 0, 0, 1, 1, 1 2, 1, 0, 1, 2, 2, 1 1, 1, 1, 2, 2, 2, 1 This is double-or-nothing in columns, 4, 6 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 1, 2 2, 2, 0, 0, 1, 1, 1 2, 1, 0, 0, 2, 2, 1 1, 1, 1, 2, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 1, 2 2, 2, 0, 0, 1, 1, 1 2, 1, 0, 2, 2, 2, 1 1, 1, 1, 2, 2, 2, 1 ------------------------------------------------ Detailed Solution to problem number, 22 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 2, 0, 0 2, 0, 0, 0, 1, 0, 0 1, 2, 2, 1, 1, 2, 0 1, 1, 2, 1, 1, 2, 0 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 2, 0, 0 2, 0, 0, 1, 1, 0, 0 1, 2, 2, 1, 1, 2, 0 1, 1, 2, 1, 1, 2, 0 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 2, 0, 0 2, 0, 0, 1, 1, 0, 0 1, 2, 2, 1, 1, 2, 0 1, 1, 2, 1, 1, 2, 0 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 2, 0, 0 2, 0, 1, 1, 1, 0, 0 1, 2, 2, 1, 1, 2, 0 1, 1, 2, 1, 1, 2, 0 This is double-or-nothing in columns, 2, 6 ------------------------------------------------ Detailed Solution to problem number, 23 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 1, 0, 0 2, 1, 1, 2, 2, 2, 1 2, 1, 2, 2, 1, 1, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 1, 1, 0, 0 2, 1, 1, 2, 2, 2, 1 2, 1, 2, 2, 1, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 2, 1, 1, 0, 0 2, 1, 1, 2, 2, 2, 1 2, 1, 2, 2, 1, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 7 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 2, 1, 1, 0, 1 2, 1, 1, 2, 2, 2, 1 2, 1, 2, 2, 1, 1, 1 This is double-or-nothing in columns, 6, 7 ------------------------------------------------ Detailed Solution to problem number, 24 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 0, 2 2, 1, 2, 0, 1, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 1, 2, 3, 4, 5, 6, 7 If Black goes in column, 1, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 2, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 Red can win immediately by moving in column, 1 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 0, 0, 0, 1 2, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 If Black goes in column, 2, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 1, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 6 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 1, 1, 2, 2 2, 1, 2, 1, 1, 2, 1 Red can win immediately by moving in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 1, 2 2, 2, 1, 1, 1, 2, 2 2, 1, 2, 1, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 1, 2 2, 1, 2, 1, 1, 2, 1 This is double-or-nothing in columns, 4, 6 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 1, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 This is double-or-nothing in columns, 2, 6 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 1, 2 2, 1, 2, 1, 1, 2, 1 This is double-or-nothing in columns, 4, 6 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 2, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 1 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 1, 1, 1, 0, 2, 0, 2 2, 2, 1, 2, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 This is double-or-nothing in columns, 1, 4 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 1, 1, 1, 2, 0, 2 2, 2, 1, 2, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 This is double-or-nothing in columns, 1, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 1, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 This is double-or-nothing in columns, 2, 6 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 1, 2 2, 1, 2, 1, 1, 2, 1 This is double-or-nothing in columns, 4, 6 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 2, 2 2, 1, 2, 1, 1, 2, 1 Red can win immediately by moving in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 1, 2 2, 2, 1, 0, 1, 2, 2 2, 1, 2, 1, 1, 2, 1 If Black goes in column, 7, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 0, 0, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 0, 0, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 1, 1, 0, 2 2, 1, 2, 1, 1, 2, 1 This is double-or-nothing in columns, 2, 6 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 0, 0, 0, 0, 0, 0, 1 0, 1, 1, 0, 2, 0, 2 2, 2, 1, 0, 1, 1, 2 2, 1, 2, 1, 1, 2, 1 This is double-or-nothing in columns, 4, 6 ------------------------------------------------ Detailed Solution to problem number, 25 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 0, 0, 1, 0, 0 1, 1, 2, 2, 1, 1, 2 2, 2, 2, 1, 2, 1, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 0, 1, 1, 0, 0 1, 1, 2, 2, 1, 1, 2 2, 2, 2, 1, 2, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 2, 0, 0 0, 0, 0, 1, 1, 0, 0 1, 1, 2, 2, 1, 1, 2 2, 2, 2, 1, 2, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 2, 0, 0 0, 1, 0, 1, 1, 0, 0 1, 1, 2, 2, 1, 1, 2 2, 2, 2, 1, 2, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 2, 0, 0 0, 1, 2, 1, 1, 0, 0 1, 1, 2, 2, 1, 1, 2 2, 2, 2, 1, 2, 1, 1 Red can win immediately by moving in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 2, 2, 0, 0 0, 1, 2, 1, 1, 0, 0 1, 1, 2, 2, 1, 1, 2 2, 2, 2, 1, 2, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 2, 0, 0 0, 0, 1, 1, 1, 0, 0 1, 1, 2, 2, 1, 1, 2 2, 2, 2, 1, 2, 1, 1 This is double-or-nothing in columns, 2, 3, 6 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 2, 0, 0 0, 0, 0, 1, 1, 1, 0 1, 1, 2, 2, 1, 1, 2 2, 2, 2, 1, 2, 1, 1 This is double-or-nothing in columns, 3, 6, 7 ------------------------------------------------ Detailed Solution to problem number, 26 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 1 2, 2, 1, 0, 0, 1, 2 2, 2, 2, 0, 0, 1, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 1 2, 2, 1, 0, 0, 1, 2 2, 2, 2, 1, 0, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 1 2, 2, 1, 0, 0, 1, 2 2, 2, 2, 1, 2, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 1 2, 2, 1, 1, 0, 1, 2 2, 2, 2, 1, 2, 1, 1 This is double-or-nothing in columns, 4, 5 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 1 2, 2, 1, 0, 1, 1, 2 2, 2, 2, 1, 2, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 1, 1, 0, 0, 2, 1 2, 2, 1, 2, 1, 1, 2 2, 2, 2, 1, 2, 1, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 1, 1, 1, 0, 2, 1 2, 2, 1, 2, 1, 1, 2 2, 2, 2, 1, 2, 1, 1 ------------------------------------------------ Detailed Solution to problem number, 27 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 0, 0, 2 2, 1, 1, 2, 1, 0, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 1 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 0, 0, 2 2, 1, 1, 2, 1, 0, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 1, 2, 3, 4, 5, 6, 7 If Black goes in column, 1, then the position is 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 0, 0, 2 2, 1, 1, 2, 1, 0, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 2, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 1, 0, 0 2, 1, 1, 1, 2, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 If Black goes in column, 2, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 2, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 0, 0, 2 2, 1, 1, 2, 1, 0, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 2, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 2, 2, 0, 0, 0, 0 2, 1, 1, 1, 2, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 2, 2, 0, 1, 0, 0 2, 1, 1, 1, 2, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 0, 0, 2 2, 1, 1, 2, 1, 0, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 2, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 1, 0, 2, 0, 1, 0, 0 2, 1, 1, 1, 2, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 2, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 0, 0, 2 2, 1, 1, 2, 1, 0, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 2, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 2, 0, 0, 0 2, 1, 1, 1, 2, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 2, 1, 0, 0 2, 1, 1, 1, 2, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 2, 0, 2 2, 1, 1, 2, 1, 0, 1 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 1, 0, 0 2, 2, 1, 2, 2, 0, 2 2, 1, 1, 2, 1, 0, 1 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 0, 0, 2 2, 1, 1, 2, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 2, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 2, 1 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 1, 0, 0 2, 1, 1, 1, 2, 0, 0 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 2, 1 If Black goes in column, 7, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 2 2, 2, 1, 2, 0, 0, 2 2, 1, 1, 2, 1, 0, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 0, 0, 2 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 0, 0, 0 2, 1, 1, 1, 2, 0, 2 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 2, 0, 1, 0, 0 2, 1, 1, 1, 2, 0, 2 2, 2, 1, 2, 1, 0, 2 2, 1, 1, 2, 1, 0, 1 ------------------------------------------------ Detailed Solution to problem number, 28 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 0, 0, 2, 0, 2, 1, 2 0, 0, 1, 0, 1, 2, 1 2, 1, 1, 0, 2, 2, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 0 0, 0, 2, 0, 2, 1, 2 0, 0, 1, 0, 1, 2, 1 2, 1, 1, 1, 2, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 7 If Black goes in column, 7, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 2 0, 0, 2, 0, 2, 1, 2 0, 0, 1, 0, 1, 2, 1 2, 1, 1, 1, 2, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 2 0, 0, 2, 0, 2, 1, 2 0, 1, 1, 0, 1, 2, 1 2, 1, 1, 1, 2, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 2 0, 0, 2, 0, 2, 1, 2 0, 1, 1, 2, 1, 2, 1 2, 1, 1, 1, 2, 2, 2 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 2 0, 0, 2, 1, 2, 1, 2 0, 1, 1, 2, 1, 2, 1 2, 1, 1, 1, 2, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 1, 2 0, 0, 2, 0, 2, 1, 2 0, 0, 1, 1, 1, 2, 1 2, 1, 1, 1, 2, 2, 2 This is double-or-nothing in columns, 2, 4 ------------------------------------------------ Detailed Solution to problem number, 29 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 2, 0, 0 0, 0, 1, 0, 1, 0, 0 1, 2, 1, 1, 1, 0, 2 2, 1, 1, 2, 2, 0, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 2, 0, 0 0, 0, 1, 0, 1, 0, 0 1, 2, 1, 1, 1, 0, 2 2, 1, 1, 2, 2, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 6 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 2, 0, 0 0, 0, 1, 0, 1, 0, 0 1, 2, 1, 1, 1, 2, 2 2, 1, 1, 2, 2, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 2, 0, 0 0, 0, 1, 1, 1, 0, 0 1, 2, 1, 1, 1, 2, 2 2, 1, 1, 2, 2, 1, 2 This is double-or-nothing in columns, 2, 6 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 2, 0, 0 0, 0, 1, 0, 1, 1, 0 1, 2, 1, 1, 1, 2, 2 2, 1, 1, 2, 2, 1, 2 This is double-or-nothing in columns, 4, 6 ------------------------------------------------ Detailed Solution to problem number, 30 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 2, 0 2, 2, 2, 1, 2, 1, 2 1, 1, 1, 2, 2, 1, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 1, 2, 0 2, 2, 2, 1, 2, 1, 2 1, 1, 1, 2, 2, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 6 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 0, 1, 0, 0, 1, 2, 0 2, 2, 2, 1, 2, 1, 2 1, 1, 1, 2, 2, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 0, 1, 1, 0, 1, 2, 0 2, 2, 2, 1, 2, 1, 2 1, 1, 1, 2, 2, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 0, 1, 1, 2, 1, 2, 0 2, 2, 2, 1, 2, 1, 2 1, 1, 1, 2, 2, 1, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 1, 0, 2, 0 0, 1, 1, 2, 1, 2, 0 2, 2, 2, 1, 2, 1, 2 1, 1, 1, 2, 2, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 0, 1, 0, 1, 1, 2, 0 2, 2, 2, 1, 2, 1, 2 1, 1, 1, 2, 2, 1, 1 This is double-or-nothing in columns, 3, 4 ------------------------------------------------ Detailed Solution to problem number, 31 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 0, 2 0, 1, 0, 0, 0, 0, 2 0, 1, 1, 2, 1, 0, 1 2, 1, 1, 1, 2, 2, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 0, 2 0, 1, 1, 0, 0, 0, 2 0, 1, 1, 2, 1, 0, 1 2, 1, 1, 1, 2, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 2 0, 1, 1, 0, 0, 0, 2 0, 1, 1, 2, 1, 0, 1 2, 1, 1, 1, 2, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 2 0, 1, 1, 1, 0, 0, 2 0, 1, 1, 2, 1, 0, 1 2, 1, 1, 1, 2, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 2 0, 1, 1, 1, 2, 0, 2 0, 1, 1, 2, 1, 0, 1 2, 1, 1, 1, 2, 2, 2 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 1, 0, 2 0, 1, 1, 1, 2, 0, 2 0, 1, 1, 2, 1, 0, 1 2, 1, 1, 1, 2, 2, 2 ------------------------------------------------ Detailed Solution to problem number, 32 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 0, 2 0, 2, 0, 0, 0, 0, 1 1, 1, 0, 0, 2, 1, 2 2, 1, 2, 2, 1, 1, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 0, 2 0, 2, 0, 0, 0, 1, 1 1, 1, 0, 0, 2, 1, 2 2, 1, 2, 2, 1, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 6 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 2, 2 0, 2, 0, 0, 0, 1, 1 1, 1, 0, 0, 2, 1, 2 2, 1, 2, 2, 1, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 2, 2 0, 2, 0, 0, 0, 1, 1 1, 1, 0, 1, 2, 1, 2 2, 1, 2, 2, 1, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 2, 2 0, 2, 0, 0, 0, 1, 1 1, 1, 2, 1, 2, 1, 2 2, 1, 2, 2, 1, 1, 2 Red can win immediately by moving in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 2, 2 0, 2, 1, 0, 0, 1, 1 1, 1, 2, 1, 2, 1, 2 2, 1, 2, 2, 1, 1, 2 ------------------------------------------------ Detailed Solution to problem number, 33 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 2, 1, 0, 0, 1, 0, 2 2, 2, 0, 0, 1, 0, 2 1, 1, 2, 1, 2, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 2, 1, 0, 0, 1, 0, 2 2, 2, 0, 0, 1, 1, 2 1, 1, 2, 1, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 6 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 2, 1, 0, 0, 1, 2, 2 2, 2, 0, 0, 1, 1, 2 1, 1, 2, 1, 2, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 2, 1, 0, 0, 1, 2, 2 2, 2, 1, 0, 1, 1, 2 1, 1, 2, 1, 2, 2, 1 This is double-or-nothing in columns, 1, 4 ------------------------------------------------ Detailed Solution to problem number, 34 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 0, 0 0, 0, 1, 0, 0, 0, 0 2, 1, 2, 2, 2, 1, 1 2, 2, 1, 2, 2, 1, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 0, 0 0, 0, 1, 0, 0, 1, 0 2, 1, 2, 2, 2, 1, 1 2, 2, 1, 2, 2, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 6 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 2, 0 0, 0, 1, 0, 0, 1, 0 2, 1, 2, 2, 2, 1, 1 2, 2, 1, 2, 2, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 2, 0 0, 0, 1, 0, 1, 1, 0 2, 1, 2, 2, 2, 1, 1 2, 2, 1, 2, 2, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 2, 0 0, 0, 1, 2, 1, 1, 0 2, 1, 2, 2, 2, 1, 1 2, 2, 1, 2, 2, 1, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 1, 0, 2, 0 0, 0, 1, 2, 1, 1, 0 2, 1, 2, 2, 2, 1, 1 2, 2, 1, 2, 2, 1, 1 ------------------------------------------------ Detailed Solution to problem number, 35 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 0, 1, 0, 0 2, 2, 2, 1, 2, 1, 1 1, 2, 1, 2, 1, 2, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 0, 1, 1, 0 2, 2, 2, 1, 2, 1, 1 1, 2, 1, 2, 1, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 6 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 1, 0, 0, 0, 1, 1, 0 2, 2, 2, 1, 2, 1, 1 1, 2, 1, 2, 1, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 1, 0, 0, 1, 1, 1, 0 2, 2, 2, 1, 2, 1, 1 1, 2, 1, 2, 1, 2, 2 This is double-or-nothing in columns, 3, 7 ------------------------------------------------ Detailed Solution to problem number, 36 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 0, 0 2, 2, 0, 0, 1, 0, 0 2, 1, 1, 2, 2, 1, 0 1, 2, 2, 2, 1, 1, 0 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 0, 0 2, 2, 0, 0, 1, 1, 0 2, 1, 1, 2, 2, 1, 0 1, 2, 2, 2, 1, 1, 0 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 6 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 2, 0 2, 2, 0, 0, 1, 1, 0 2, 1, 1, 2, 2, 1, 0 1, 2, 2, 2, 1, 1, 0 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 2, 0 2, 2, 1, 0, 1, 1, 0 2, 1, 1, 2, 2, 1, 0 1, 2, 2, 2, 1, 1, 0 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 2, 0 2, 2, 1, 2, 1, 1, 0 2, 1, 1, 2, 2, 1, 0 1, 2, 2, 2, 1, 1, 0 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 0, 1, 0, 2, 0 2, 2, 1, 2, 1, 1, 0 2, 1, 1, 2, 2, 1, 0 1, 2, 2, 2, 1, 1, 0 ------------------------------------------------ Detailed Solution to problem number, 37 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 0, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 7 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 0, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 1, 2, 3, 4, 5, 6, 7 If Black goes in column, 1, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 2, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 0, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 2, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 1, 1, 1, 0, 2, 1 This is double-or-nothing in columns, 2, 5 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 2, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 1, 2, 1 This is double-or-nothing in columns, 2, 5 If Black goes in column, 2, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 2, 1, 1, 0, 2, 1 Red can win immediately by moving in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 1, 1, 1, 0, 1, 2 2, 2, 1, 1, 0, 2, 1 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 0, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 1, 1, 1, 0, 2, 1 This is double-or-nothing in columns, 2, 5 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 1, 2, 1 This is double-or-nothing in columns, 2, 5 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 2, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 0, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 2, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 1, 1, 1, 0, 2, 1 This is double-or-nothing in columns, 2, 5 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 2, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 1, 2, 1 This is double-or-nothing in columns, 2, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 2, 2, 1 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 1, 1, 2 2, 0, 1, 1, 2, 2, 1 If Black goes in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 2, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 0, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 2, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 1, 1, 1, 0, 2, 1 This is double-or-nothing in columns, 2, 5 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 2, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 1, 2, 1 This is double-or-nothing in columns, 2, 5 If Black goes in column, 7, then the position is 0, 0, 0, 0, 0, 0, 2 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 0, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 2 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 1, 1, 1, 0, 2, 1 This is double-or-nothing in columns, 2, 5 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 2 0, 0, 0, 0, 0, 0, 1 0, 0, 1, 0, 0, 0, 2 2, 0, 2, 0, 0, 2, 2 1, 0, 1, 1, 0, 1, 2 2, 0, 1, 1, 1, 2, 1 This is double-or-nothing in columns, 2, 5 ------------------------------------------------ Detailed Solution to problem number, 38 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 2, 0, 0, 0 2, 0, 0, 1, 0, 0, 0 2, 2, 0, 1, 1, 2, 1 1, 2, 0, 1, 1, 2, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 2, 0, 0, 0 2, 0, 0, 1, 1, 0, 0 2, 2, 0, 1, 1, 2, 1 1, 2, 0, 1, 1, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 2, 2, 0, 0 2, 0, 0, 1, 1, 0, 0 2, 2, 0, 1, 1, 2, 1 1, 2, 0, 1, 1, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 2, 2, 0, 0 2, 0, 0, 1, 1, 1, 0 2, 2, 0, 1, 1, 2, 1 1, 2, 0, 1, 1, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 7 If Black goes in column, 7, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 2, 2, 0, 0 2, 0, 0, 1, 1, 1, 2 2, 2, 0, 1, 1, 2, 1 1, 2, 0, 1, 1, 2, 2 Red can win immediately by moving in column, 7 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 2, 2, 0, 1 2, 0, 0, 1, 1, 1, 2 2, 2, 0, 1, 1, 2, 1 1, 2, 0, 1, 1, 2, 2 ------------------------------------------------ Detailed Solution to problem number, 39 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 1, 2, 0, 1, 0, 2, 0 2, 1, 1, 1, 0, 1, 0 2, 1, 1, 2, 0, 2, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 1, 2, 0, 1, 0, 2, 0 2, 1, 1, 1, 0, 1, 0 2, 1, 1, 2, 1, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 1, 2, 0, 1, 0, 2, 0 2, 1, 1, 1, 2, 1, 0 2, 1, 1, 2, 1, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 1, 2, 1, 1, 0, 2, 0 2, 1, 1, 1, 2, 1, 0 2, 1, 1, 2, 1, 2, 2 This is double-or-nothing in columns, 2, 3 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 1, 2, 0, 1, 1, 2, 0 2, 1, 1, 1, 2, 1, 0 2, 1, 1, 2, 1, 2, 2 This is double-or-nothing in columns, 5, 6 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 1, 0 1, 2, 0, 1, 0, 2, 0 2, 1, 1, 1, 2, 1, 0 2, 1, 1, 2, 1, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 1, 0 1, 2, 0, 1, 2, 2, 0 2, 1, 1, 1, 2, 1, 0 2, 1, 1, 2, 1, 2, 2 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 1, 1, 0 1, 2, 0, 1, 2, 2, 0 2, 1, 1, 1, 2, 1, 0 2, 1, 1, 2, 1, 2, 2 ------------------------------------------------ Detailed Solution to problem number, 40 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 1, 0, 2, 0, 2 2, 0, 1, 0, 1, 2, 1 1, 1, 2, 2, 1, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 1, 0, 2, 0, 2 2, 1, 1, 0, 1, 2, 1 1, 1, 2, 2, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 1, 0, 2, 0, 2 2, 1, 1, 2, 1, 2, 1 1, 1, 2, 2, 1, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 1, 1, 2, 0, 2 2, 1, 1, 2, 1, 2, 1 1, 1, 2, 2, 1, 2, 1 This is double-or-nothing in columns, 4, 5 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 0, 0 2, 0, 1, 0, 2, 0, 2 2, 1, 1, 2, 1, 2, 1 1, 1, 2, 2, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 1, 0, 0 2, 0, 1, 2, 2, 0, 2 2, 1, 1, 2, 1, 2, 1 1, 1, 2, 2, 1, 2, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 1, 1, 0, 0 2, 0, 1, 2, 2, 0, 2 2, 1, 1, 2, 1, 2, 1 1, 1, 2, 2, 1, 2, 1 ------------------------------------------------ Detailed Solution to problem number, 41 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 1, 0, 0, 0, 0, 1, 0 2, 2, 1, 1, 0, 2, 1 2, 2, 1, 2, 1, 1, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 2, 0 1, 0, 1, 0, 0, 1, 0 2, 2, 1, 1, 0, 2, 1 2, 2, 1, 2, 1, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 2, 0 1, 0, 1, 0, 0, 1, 0 2, 2, 1, 1, 0, 2, 1 2, 2, 1, 2, 1, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 2, 0 1, 1, 1, 0, 0, 1, 0 2, 2, 1, 1, 0, 2, 1 2, 2, 1, 2, 1, 1, 2 This is double-or-nothing in columns, 2, 4 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 2, 0 1, 0, 1, 1, 0, 1, 0 2, 2, 1, 1, 0, 2, 1 2, 2, 1, 2, 1, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 2 If Black goes in column, 2, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 2, 0 1, 2, 1, 1, 0, 1, 0 2, 2, 1, 1, 0, 2, 1 2, 2, 1, 2, 1, 1, 2 Red can win immediately by moving in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 1, 2, 0, 0, 2, 0 1, 2, 1, 1, 0, 1, 0 2, 2, 1, 1, 0, 2, 1 2, 2, 1, 2, 1, 1, 2 ------------------------------------------------ Detailed Solution to problem number, 42 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 0, 0 0, 1, 0, 0, 0, 0, 0 2, 2, 1, 2, 1, 2, 1 1, 2, 1, 1, 2, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 0, 0, 0, 0, 0 0, 1, 1, 0, 0, 0, 0 2, 2, 1, 2, 1, 2, 1 1, 2, 1, 1, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 0, 1, 1, 0, 0, 0, 0 2, 2, 1, 2, 1, 2, 1 1, 2, 1, 1, 2, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 1 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 0, 0 2, 2, 1, 2, 1, 2, 1 1, 2, 1, 1, 2, 2, 1 This is double-or-nothing in columns, 1, 4 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 0, 1, 1, 1, 0, 0, 0 2, 2, 1, 2, 1, 2, 1 1, 2, 1, 1, 2, 2, 1 This is double-or-nothing in columns, 1, 5 ------------------------------------------------ Detailed Solution to problem number, 43 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 0, 1, 0, 0 1, 1, 2, 1, 1, 2, 1 2, 2, 2, 1, 2, 2, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 1, 0, 0, 1, 1, 0, 0 1, 1, 2, 1, 1, 2, 1 2, 2, 2, 1, 2, 2, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 1, 0, 0, 1, 1, 0, 0 1, 1, 2, 1, 1, 2, 1 2, 2, 2, 1, 2, 2, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 1, 0, 1, 1, 1, 0, 0 1, 1, 2, 1, 1, 2, 1 2, 2, 2, 1, 2, 2, 2 This is double-or-nothing in columns, 2, 6 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 1, 0, 0, 1, 1, 1, 0 1, 1, 2, 1, 1, 2, 1 2, 2, 2, 1, 2, 2, 2 This is double-or-nothing in columns, 3, 7 ------------------------------------------------ Detailed Solution to problem number, 44 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 1 0, 0, 0, 1, 0, 0, 2 0, 2, 1, 1, 2, 2, 2 0, 1, 1, 2, 1, 1, 2 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 1 0, 0, 0, 1, 1, 0, 2 0, 2, 1, 1, 2, 2, 2 0, 1, 1, 2, 1, 1, 2 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 2, 0, 1 0, 0, 0, 1, 1, 0, 2 0, 2, 1, 1, 2, 2, 2 0, 1, 1, 2, 1, 1, 2 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 2, 0, 1 0, 0, 1, 1, 1, 0, 2 0, 2, 1, 1, 2, 2, 2 0, 1, 1, 2, 1, 1, 2 This is double-or-nothing in columns, 2, 3, 6 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 6 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 2, 0, 1 0, 0, 0, 1, 1, 1, 2 0, 2, 1, 1, 2, 2, 2 0, 1, 1, 2, 1, 1, 2 This is double-or-nothing in columns, 3, 6 ------------------------------------------------ Detailed Solution to problem number, 45 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 1, 0, 1, 2 0, 0, 0, 2, 0, 1, 1 0, 1, 0, 1, 0, 2, 2 2, 2, 1, 2, 0, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 1, 0, 1, 2 0, 0, 0, 2, 0, 1, 1 0, 1, 1, 1, 0, 2, 2 2, 2, 1, 2, 0, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 1 If Black goes in column, 1, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 1, 0, 1, 2 0, 0, 0, 2, 0, 1, 1 2, 1, 1, 1, 0, 2, 2 2, 2, 1, 2, 0, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 1, 0, 1, 2 0, 0, 0, 2, 0, 1, 1 2, 1, 1, 1, 0, 2, 2 2, 2, 1, 2, 1, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 1, 0, 1, 2 0, 0, 0, 2, 0, 1, 1 2, 1, 1, 1, 2, 2, 2 2, 2, 1, 2, 1, 2, 1 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 1, 0, 1, 2 0, 0, 0, 2, 1, 1, 1 2, 1, 1, 1, 2, 2, 2 2, 2, 1, 2, 1, 2, 1 ------------------------------------------------ Detailed Solution to problem number, 46 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 0, 1, 0, 0, 0, 0 2, 1, 1, 2, 1, 1, 2 2, 1, 2, 1, 2, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 2 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 0, 0, 0 0, 1, 1, 0, 0, 0, 0 2, 1, 1, 2, 1, 1, 2 2, 1, 2, 1, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 2 If Black goes in column, 2, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 0, 1, 1, 0, 0, 0, 0 2, 1, 1, 2, 1, 1, 2 2, 1, 2, 1, 2, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 1 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 1, 1, 1, 0, 0, 0, 0 2, 1, 1, 2, 1, 1, 2 2, 1, 2, 1, 2, 2, 1 This is double-or-nothing in columns, 1, 4 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 0, 1, 1, 1, 0, 0, 0 2, 1, 1, 2, 1, 1, 2 2, 1, 2, 1, 2, 2, 1 This is double-or-nothing in columns, 1, 5 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 0, 1, 1, 0, 1, 0, 0 2, 1, 1, 2, 1, 1, 2 2, 1, 2, 1, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 4 If Black goes in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 0, 0, 0, 0 0, 1, 1, 2, 1, 0, 0 2, 1, 1, 2, 1, 1, 2 2, 1, 2, 1, 2, 2, 1 Red can win immediately by moving in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 2, 2, 1, 0, 0, 0 0, 1, 1, 2, 1, 0, 0 2, 1, 1, 2, 1, 1, 2 2, 1, 2, 1, 2, 2, 1 ------------------------------------------------ Detailed Solution to problem number, 47 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 0, 0, 1, 0, 0 2, 2, 1, 2, 1, 2, 2 2, 1, 1, 1, 2, 1, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 3 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 2, 0, 0 0, 0, 1, 0, 1, 0, 0 2, 2, 1, 2, 1, 2, 2 2, 1, 1, 1, 2, 1, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 3 If Black goes in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 2, 0, 0 0, 0, 1, 0, 1, 0, 0 2, 2, 1, 2, 1, 2, 2 2, 1, 1, 1, 2, 1, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 2, 0, 2, 0, 0 0, 0, 1, 1, 1, 0, 0 2, 2, 1, 2, 1, 2, 2 2, 1, 1, 1, 2, 1, 1 This is double-or-nothing in columns, 2, 6 ------------------------------------------------ Detailed Solution to problem number, 48 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 1, 2 0, 2, 1, 0, 0, 2, 2 0, 2, 2, 0, 0, 1, 1 0, 1, 1, 0, 2, 2, 1 --------------------------------------------------- Red wins in, 3, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 1, 2 0, 2, 1, 0, 0, 2, 2 0, 2, 2, 0, 0, 1, 1 0, 1, 1, 1, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 1 If Black goes in column, 1, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 1, 2 0, 2, 1, 0, 0, 2, 2 0, 2, 2, 0, 0, 1, 1 2, 1, 1, 1, 2, 2, 1 --------------------------------------------------- Red wins in, 2, moves by putting its piece(1) in column, 4 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 1, 2 0, 2, 1, 0, 0, 2, 2 0, 2, 2, 1, 0, 1, 1 2, 1, 1, 1, 2, 2, 1 Indeed, the reasonable moves of Black are to place its piece(2) in columns, 5 If Black goes in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 1, 2 0, 2, 1, 0, 0, 2, 2 0, 2, 2, 1, 2, 1, 1 2, 1, 1, 1, 2, 2, 1 Red can win immediately by moving in column, 5 resulting in position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 0, 0, 1, 0, 0, 1, 2 0, 2, 1, 0, 1, 2, 2 0, 2, 2, 1, 2, 1, 1 2, 1, 1, 1, 2, 2, 1