Answer to question #11: Opening a Safe Without the Combination

11. You are to open a safe without knowing the combination. Beginning with the dial set at zero, the dial must be turned counter-clockwise to the first combination number, (then clockwise back to zero), and clockwise to the second combination number, (then counter-clockwise back to zero), and counter-clockwise again to the third and final number, where upon the door shall immediately spring open. There are 40 numbers on the dial, including the zero.

Without knowing the combination numbers, what is the maximum number of trials required to open the safe (one trial equals one attempt to dial a full three-number combination)?

There isn't a great deal of working out here you sort of get it or you don't...

a dial from a combination safe 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 sum.

The key word here is 'immediately.' The implication of this is that you do not have to test each three number combination.

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 'the door shall immediately spring open.'

If that hasn't cleared it up the answer is below:-

40 x 40 = 1600

This is a clear example of a puzzle with a very carefully worded question that needs close attention. Both the 'immediately open' and that the dial returns to zero are conspicuous.

Is that definitely the answer?

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.)





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