This is a sample of Capsule puzzles, invented by Wei-Hwa Huang, and published (starting end of 2016) in the New York times and their solution by Shalosh B. Ekhad, using the Maple package Capsules.txt, available from Doron Zeilbegrer's website http://www.math.rutgers.edu/~zeilberg/tokhniot/Capsules.txt ----------------------------- For the Dec. 25, 2016 New York Times Capsule Puzzle: You have a 7 by 7 rectangle with the following clues [3 0 2 0 0 0 0] [ ] [5 7 0 0 0 5 0] [ ] [0 0 0 5 3 0 0] [ ] [1 6 0 0 0 7 2] [ ] [0 0 5 2 0 0 0] [ ] [0 2 0 0 0 6 2] [ ] [0 0 0 0 5 0 7] There are , 10, capsules , here they are We now list the capsules, where the cells are indicated by pairs [i,j], wher\ e [i,j] means the the cell that is in the i-th row and j-th column, as in matrix notation (reading from left to right and top to b\ ottom The , 1, -th capsule consists of the cells {[1, 1], [1, 2], [1, 3], [1, 4], [2, 2], [2, 4], [2, 5]} The , 2, -th capsule consists of the cells {[1, 5], [1, 6], [2, 6], [2, 7], [3, 5], [3, 6], [4, 6]} The , 3, -th capsule consists of the cells {[1, 7]} The , 4, -th capsule consists of the cells {[2, 1], [2, 3], [3, 1], [3, 2], [3, 3], [4, 1], [5, 1]} The , 5, -th capsule consists of the cells {[3, 4], [4, 3], [4, 4], [4, 5], [5, 4]} The , 6, -th capsule consists of the cells {[3, 7], [4, 7]} The , 7, -th capsule consists of the cells {[4, 2], [5, 2], [5, 3], [6, 1], [6, 2], [7, 2], [7, 3]} The , 8, -th capsule consists of the cells {[5, 5], [5, 6], [5, 7], [6, 5], [6, 7]} The , 9, -th capsule consists of the cells {[6, 3], [6, 4], [6, 6], [7, 4], [7, 5], [7, 6], [7, 7]} The , 10, -th capsule consists of the cells {[7, 1]} The solutions is [3 1 2 5 1 2 1] [ ] [5 7 6 4 6 5 6] [ ] [3 4 2 5 3 4 1] [ ] [1 6 3 4 1 7 2] [ ] [7 4 5 2 5 4 1] [ ] [3 2 3 4 3 6 2] [ ] [1 7 1 2 5 1 7] ------------------------------------------- For the Jan. 1, 2017 New York Times Capsule Puzzle: You have a 7 by 7 rectangle with the following clues [0 0 4 0 5 0 4] [ ] [1 0 0 0 0 3 0] [ ] [0 0 0 0 0 0 1] [ ] [0 0 3 2 1 0 0] [ ] [4 0 0 0 0 0 0] [ ] [0 5 0 0 0 0 3] [ ] [3 0 4 0 3 0 0] There are , 11, capsules , here they are We now list the capsules, where the cells are indicated by pairs [i,j], wher\ e [i,j] means the the cell that is in the i-th row and j-th column, as in matrix notation (reading from left to right and top to b\ ottom The , 1, -th capsule consists of the cells {[1, 1], [2, 1]} The , 2, -th capsule consists of the cells {[1, 2], [1, 3], [1, 4], [1, 5], [2, 3]} The , 3, -th capsule consists of the cells {[1, 6], [1, 7], [2, 5], [2, 6], [3, 5]} The , 4, -th capsule consists of the cells {[2, 2], [3, 1], [3, 2], [3, 3], [4, 3]} The , 5, -th capsule consists of the cells {[2, 4], [3, 4], [4, 4], [5, 4], [6, 4]} The , 6, -th capsule consists of the cells {[2, 7], [3, 7]} The , 7, -th capsule consists of the cells {[3, 6], [4, 5], [4, 6], [4, 7], [5, 5]} The , 8, -th capsule consists of the cells {[4, 1], [4, 2], [5, 1], [5, 2], [6, 1]} The , 9, -th capsule consists of the cells {[5, 3], [6, 2], [6, 3], [7, 1], [7, 2]} The , 10, -th capsule consists of the cells {[5, 6], [5, 7], [6, 6], [6, 7], [7, 7]} The , 11, -th capsule consists of the cells {[6, 5], [7, 3], [7, 4], [7, 5], [7, 6]} The solutions is [2 3 4 1 5 1 4] [ ] [1 5 2 3 2 3 2] [ ] [2 4 1 4 5 4 1] [ ] [3 5 3 2 1 2 5] [ ] [4 1 4 5 3 4 1] [ ] [2 5 2 1 2 5 3] [ ] [3 1 4 5 3 1 2] ------------------------------------------- For the Feb. 5, 2017 New York Times Capsule Puzzle: You have a 7 by 7 rectangle with the following clues [0 1 0 5 0 0 0] [ ] [2 0 0 3 0 0 4] [ ] [0 0 0 0 0 0 0] [ ] [7 5 0 0 0 6 5] [ ] [0 0 0 0 0 0 0] [ ] [3 0 0 7 0 0 5] [ ] [0 0 0 2 0 3 0] There are , 13, capsules , here they are We now list the capsules, where the cells are indicated by pairs [i,j], wher\ e [i,j] means the the cell that is in the i-th row and j-th column, as in matrix notation (reading from left to right and top to b\ ottom The , 1, -th capsule consists of the cells {[1, 1], [1, 2], [2, 1]} The , 2, -th capsule consists of the cells {[1, 3], [1, 4], [2, 2], [2, 3], [3, 1], [3, 2], [4, 1]} The , 3, -th capsule consists of the cells {[1, 5], [1, 6], [2, 5]} The , 4, -th capsule consists of the cells {[1, 7], [2, 6], [2, 7], [3, 5], [3, 6]} The , 5, -th capsule consists of the cells {[2, 4], [3, 3], [3, 4], [4, 2], [4, 3]} The , 6, -th capsule consists of the cells {[3, 7]} The , 7, -th capsule consists of the cells {[4, 4], [4, 5], [5, 4]} The , 8, -th capsule consists of the cells {[4, 6], [4, 7], [5, 5], [5, 6], [6, 4], [6, 5], [7, 4]} The , 9, -th capsule consists of the cells {[5, 1], [5, 2], [6, 1]} The , 10, -th capsule consists of the cells {[5, 3], [6, 2], [6, 3], [7, 1], [7, 2]} The , 11, -th capsule consists of the cells {[5, 7], [6, 6], [6, 7], [7, 5], [7, 6]} The , 12, -th capsule consists of the cells {[7, 3]} The , 13, -th capsule consists of the cells {[7, 7]} The solutions is [3 1 2 5 2 3 1] [ ] [2 4 6 3 1 5 4] [ ] [1 3 2 4 2 3 1] [ ] [7 5 1 3 1 6 5] [ ] [1 2 4 2 4 3 1] [ ] [3 5 3 7 1 2 5] [ ] [1 2 1 2 4 3 1] ------------------------------------------- For the March 19, 2017 New York Times Capsule Puzzle: You have a 7 by 7 rectangle with the following clues [0 0 0 0 0 0 3] [ ] [0 0 0 0 2 0 0] [ ] [0 0 0 0 0 6 0] [ ] [0 0 0 0 0 0 0] [ ] [0 4 0 0 0 0 0] [ ] [0 0 3 0 0 0 0] [ ] [2 0 0 2 0 0 0] There are , 12, capsules , here they are We now list the capsules, where the cells are indicated by pairs [i,j], where [i,j] means the the cell that is in the i-th row and j-th column, as in matrix notation (reading from left to right and top to bottom The , 1, -th capsule consists of the cells {[1, 1], [1, 2], [2, 1], [2, 2]} The , 2, -th capsule consists of the cells {[1, 3], [1, 4], [2, 3], [2, 4]} The , 3, -th capsule consists of the cells {[1, 5], [2, 5], [2, 6], [3, 5], [3, 6], [3, 7]} The , 4, -th capsule consists of the cells {[1, 6], [1, 7], [2, 7]} The , 5, -th capsule consists of the cells {[3, 1], [3, 2], [4, 1], [4, 2]} The , 6, -th capsule consists of the cells {[3, 3], [3, 4], [4, 3], [4, 4]} The , 7, -th capsule consists of the cells {[4, 5], [5, 4], [5, 5]} The , 8, -th capsule consists of the cells {[4, 6], [4, 7], [5, 6], [5, 7]} The , 9, -th capsule consists of the cells {[5, 1], [5, 2], [5, 3], [6, 1], [6, 2]} The , 10, -th capsule consists of the cells {[6, 3], [7, 1], [7, 2], [7, 3]} The , 11, -th capsule consists of the cells {[6, 4], [6, 5], [7, 4], [7, 5]} The , 12, -th capsule consists of the cells {[6, 6], [6, 7], [7, 6], [7, 7]} The solutions is [3 4 2 1 3 1 3] [ ] [2 1 3 4 2 4 2] [ ] [3 4 2 1 5 6 1] [ ] [2 1 3 4 3 4 3] [ ] [3 4 2 1 2 1 2] [ ] [1 5 3 4 3 4 3] [ ] [2 4 1 2 1 2 1] ------------------------------------------- The whole thing (to solve the above four puzzles) took, 0.632, seconds.