Re: A Permutation Quest

I didn't intend to suggest examing all permutations, though perhaps my wording of "Why not examine all cases where A = 9" made that unclear. I meant "Why not set A = 9, and then examine the possibilities for B".

To give a summary of my argument:

1) Set A = 9. Then the condition on A is guaranteed satisfied.

2) Every solution with B = x also has a solution with B = x and A = 9, since you could swap 9 and the A value for any solution where A wasn't 9, to get another solution, with the same B value (since easily B isn't 9, so it isn't being swapped), but with A = 9.

3) Consider all ways to make column 1, with numbers {1, 2, ..., 8} available, so that the B condition is satisfied. List the possible B's you get this way. This gives the answer to this problem.

4) You don't need to worry about the conditon on C, because whenever you've populated A=9 and column 1, simply set C = the minimum of the 5 remaining numbers.