Hi Mike
How about this? (original post deleted after your explanantory PM).
Assuming 'rows' are horizontal lines of numbers (if you mean columns then rotate my answer through 90 degrees to get the desired effect), and any number pair (e.g. 1 & 2 is a number pair) cannot be repeated on any other row in the grid, try doing this :
First row, start with 1 and add 1 to each number giving :
1 2 3 4 5 6 7 8 9 10
Second row, reverse the previous row to give you :
10 9 8 7 6 5 4 3 2 1
Third row, again start with 1 but add 2, once 10 reached, start again with the smallest available number again adding 2, to give this :
1 3 5 7 9 2 4 6 8 10
Row 4, reverse to get :
10 8 6 4 2 9 7 5 3 1
Row 5, again start with 1 but add 3 this time, and again restart with the smallest available number once you reach 10 to get :
1 4 7 10 2 5 8 3 6 9
Reverse to get row 6 and so on....
HTH, Andrew