## Sunday, March 6, 2011

### Without knowing the combination numbers, what is the maximum number of trials required to open the safe ..Combination Problem

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)?

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 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 'the door shall immediately spring open.'

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

40 x 40 = 1600

Source : puzzles.nigelcoldwell.co.uk/elevenhint.htm