Before reading the answer can I interest you in a clue?
Well clearly the answer is not 40x40x40 = 64000,
that would just be too easy, not so much a lateral thinking puzzle as just a
The key word here is 'immediately.' The
implication of this is that you do not have to try 40 times at the last number
for each combination of the first number two numbers.
With this in mind you see that after any combination of
the first two numbers you can, instead of trying all of the 40 possibilities
for the last number, just turn the dial all the way to the end for the last
number; in doing this you will necessarily pass the correct number where upon
shall immediately spring open.'
If that hasn't cleared it up the answer is below:-
40 x 40 = 1600
Is the answer definitely 1600? Well possibly not. There are certain combinations that might open sooner. For example if the combination were 0,0,0 the safe might well open immediately. The puzzle, whilst extremely precise in some ways doesn't give us enough information to answer these scenarios. Probably the answer is closer to 39 x 39. Notwithstanding this I maintain, that for our purposes, the key is in realising it is not 40 x 40 x 40. (Or 39 x 39 x 39 for that matter.)