Re-arrange matrix row elements so that a specific condition is fulfilled

Say we have matrix

A =

1 2 3

1 3 5

1 2 4

2 3 7

The task is the re-arrange the row elements so that in no row 2 elements are in same order. For example rows 1 and 2 both have elements 1 and 3 so that three is after one. We can fliplr row 2 indices 1:2 and we get row 3 1 5. This has to be done for all rows. The problem in my algorithm is that it is slow and it ends up flipping some rows 3 times and some indices are again in the same order as in some rows.. Maybe this could be done with Answer Set Programming..

I have attached a matrix of 25 rows as test data

[Walter Roberson]

My suspicion is that in the general case you may need to backtrack. There is a temptation to start at the top and keep all the rows that work moving from top to bottom, but I have a suspicion that if you do that you might force contradiction on some of the rows that do not originally work. I suspect that you might need to deliberately dearrange some of the "good" entries.

[Pseudoscientist]

Yes that is exactly what happens