Distribute numbers in array

This is an extension to a thread I posted earlier.

I want to sort numbers in an array that do not repeat in the same row or column. Also, the numbers in each row CANNOT be moved from that row, but CAN be moved from the column. Numbers in a column CANNOT repeat (for non-example, the number 0 is found in column one on rows 1, 8, 15, 22, 29, 36, 43, 50; for a good example, the number 49 is in different columns found in rows 1, 2, 3, 4, 5, 6, 7, 57). For your information, the numbers are listed below.

0 1 2 3 4 5 6 49
7 49 9 10 11 12 13 8
15 14 49 16 17 18 19 20
23 21 22 49 24 25 26 27
32 33 34 28 49 29 30 31
35 36 37 38 39 49 41 40
42 43 44 45 46 47 49 48
0 35 7 42 14 50 21 28
1 36 8 43 15 50 22 29
2 37 9 44 16 50 23 30
3 38 10 45 17 50 24 31
32 4 39 11 50 46 18 25
33 5 40 12 47 50 19 26
34 6 41 13 48 50 20 27
0 32 48 8 16 40 51 24
1 33 41 42 17 51 9 25
34 35 10 43 2 18 51 26
51 3 36 11 44 19 27 28
4 37 12 45 51 20 21 29
5 38 13 14 51 46 22 30
6 39 7 15 51 23 47 31
0 38 9 47 18 52 27 29
1 39 10 48 19 52 21 30
2 40 42 11 20 22 52 31
32 3 41 43 12 14 52 23
33 35 4 44 13 15 52 24
34 36 5 7 45 16 52 25
37 6 8 46 17 52 26 28
0 33 36 10 46 20 53 23
1 34 37 11 14 47 53 24
2 38 12 15 48 53 25 28
3 39 42 13 16 53 26 29
4 7 40 43 17 53 27 30
5 8 41 44 18 21 53 31
32 35 6 9 45 19 53 22
0 41 11 45 15 54 26 30
1 35 12 46 16 54 27 31
32 2 36 13 47 17 21 54
33 3 37 7 48 18 22 54
34 4 38 8 42 19 54 23
5 39 9 43 20 54 24 28
6 40 10 44 14 54 25 29
0 34 39 44 12 17 22 55
1 40 55 13 45 18 23 28
2 7 41 46 19 55 24 29
3 8 47 35 20 55 25 30
4 9 14 48 55 36 26 31
32 37 10 15 55 27 42 5
33 43 38 6 11 16 21 55
0 37 43 13 19 56 25 31
32 1 38 7 44 20 56 26
33 2 39 8 45 14 56 27
34 3 40 9 46 15 21 56
4 41 10 47 16 22 56 28
35 5 11 48 17 23 56 29
36 6 42 12 56 18 24 30
49 50 51 52 53 54 55 56

Is there a formula that can do this for me? Thanks in advance.

I must be a newb. Always returns #Name? Also, I've never used Macro: I copied and pasted your's by opening up Visual Basic Editor, selecting my sheet and then copying a pasting it. Should that do the trick?

The trick with my listed numbers is that in any given row only 1 number matches another number, hence why my numbers cannot move from their row. Just don't want the same number to appear in the same column, yet still retain that only 1 number matches another number in any given row. Hope that's clear.

Thanks thus far and for the prompt reply.

I was beating my head silly and finally thought, "I should switch from my MacBook Pro to my PC". I did that: no problems and the Latin Rectangle performed flawlessly. Thank you and thank you for your patience.

However, applying a Latin Rectangle to my array still doesn't solve my problem and I think it is because there are eight quantities of each number. This condition must be met: the array must have only 1 number from any row to be the same number in any given row. If you look at my array in the original post, row 1 with numbers 0 1 2 3 4 5 6 49, has any one (and only one) of those numbers in the remaining 56 rows. The same can be said about any other number in any other row. The Latin Rectangle solves the problem that there are no repeats of any number within a column or row, but it randomizes the numbers such that I can no longer reach the condition. The same principle I'm trying to illustrate is found in the game "Spot It!" http://www.blueorangegames.com/spotit/

Thanks in advance. You've been helpful and I appreciate your support.

I finally took the time to do it manually and got it all here. A number never repeats in the same column or row and every row will have at least 1 matching number in any given row. Couldn't find a formula to work... hopefully someone can come up with something... Thanks for your help and interest.

25 2 1 3 4 0
9 7 6 25 8 5
12 13 14 11 25 10
17 25 18 19 15 16
22 21 25 20 23 24
5 10 26 0 20 15
6 1 11 16 21 26
2 22 12 7 26 17
8 3 23 26 18 13
26 14 19 4 24 9
24 6 0 18 12 27
7 20 27 13 1 19
27 8 15 2 14 21
16 27 9 10 22 3
11 17 5 23 27 4
23 0 7 28 16 14
28 24 17 8 10 1
18 11 20 9 28 2
19 12 21 5 3 28
4 28 22 15 13 6
29 19 8 22 0 11
15 23 29 1 9 12
13 5 16 24 2 29
14 29 3 17 6 20
21 4 10 29 7 18
0 9 13 21 17 30
1 18 30 14 5 22
10 30 2 6 19 23
3 15 24 30 11 7
20 16 4 12 30 8
30 26 28 27 29 25