1. ## 12 matrices 5X5

How to place 25 integers (1, 2, 3, ...25) into 12 matrices of 5X5 subject to the following rules:
1. Each number is in the same row with any other number only two times.
2. No three numbers are in the same row more than once.

I've tried to solve this problem for weeks, but so far, I can only get 11 matrices filled. Below are four of them:

1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
21 22 23 24 25

1 7 13 19 25
2 8 14 20 21
3 9 15 16 22
4 10 11 17 23
5 6 12 18 24

1 8 15 17 24
7 14 16 23 5
13 20 22 4 6
19 21 3 10 12
25 2 9 11 18

1 14 22 10 18
8 16 4 12 25
15 23 6 19 2
17 5 13 21 9
24 7 20 3 11

2. Originally Posted by tonyloebis
How to place 25 integers (1, 2, 3, ...25) into 12 matrices of 5X5 subject to the following rules:
1. Each number is in the same row with any other number only two times.
2. No three numbers are in the same row more than once.

1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
21 22 23 24 25
I don't understand your rules. Could you please demonstrate how this matrix fits them? (As the numbers 1 to 25 are all distinct how can we have more than one of them in any row??)

-Dan

3. Originally Posted by topsquark
I don't understand your rules. Could you please demonstrate how this matrix fits them? (As the numbers 1 to 25 are all distinct how can we have more than one of them in any row??)

-Dan
No two numbers are in the same row as one another in more than two of the 12 matrices.

No three numbers are in the same row as one another in more than one of the 12 matrices.

RonL