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