HW 2		Kishan Patel		9/19/21

1)	let a matrix of nxn containing positive integersfrom 1 onwards. thus there is  matrix entries from 1 to n^2. let the sum of all entries Sn=(n^2(n^2+1))/2. As there are n rows in a nxn matrix, the magic constant can be described as the Sn/n which is n(n^2+1)/2

2)
8	1	6
3	5	7
4	9	2

3)
16	2	3	13
5	11	10	8
9	7	6	12
4	14	15	1

4)
30	39	48	1	10	19	28
38	47	7	9	18	27	29
46	6	8	17	26	35	37
5	14	16	25	34	36	45
13	15	24	33	42	44	4
21	23	32	41	43	3	12
22	31	40	49	2	11	20

5)

Deck A:1 3 5 7
Deck B:2 4 6

	1	3	5	7
2	B	A	A	A
4	B	B	A	A
6	B	B	B	A
Probability to win is Equal for both decks
50% A or B

6)
Deck A: 8 3 4
Deck B: 1 5 9
Deck C: 6 7 2

A vs B
	8	3	4
1	A	A	A
5	A	B	B
9	B	B	B
B Wins

B vs C
	1	5	9
6	C	C	B
7	C	C	B
2	C	B	B
C Wins

A vs C
	8	3	4
6	A	C	C
7	A	C	C
2	A	A	A
A Wins

This constitutes as the sucker's paradox because no one deck is truely the best, each deck is balanced by having an advantage over one deck and a disadvantage by another deck