Why 24? All possible permutations should be 16! / (2! * 2! * 2!), but he said nothing too crazy. Still, cyclic permutations would be 16, permutations that are cyclic in the 4-blocks would be 4^4 = 256... why 24? ;-)

If each group of four characters is one "unit", there are 4*3*2*1 = 24 possible arrangements of those four units.

Ah, no one is dumb, just a little bad luck is all. :)

The code was PADS-QCM5-T36C-5XJ3, I just went 4, 2, 1, and 3. I was feeling a touch Hitchiker-y so I put 4 and 2 together, and at the time I was looking at my copy of 13(1313) Dead End Drive, an old board game; a blend of Clue, and Mousetrap.