I am a teacher. Subject: statistics How many combinations of three number codes can occur with a standard combination lock? The range of possible numbers is 039 which allows 40 different possible choices each turn of the dial. Each combination requires exactly three numbers (i.e. three turns of the dial). E.g. 35405. Allow for reuse of the same number three times e.g.101010. I don't think there is any preference shown for certain number combinations. Can you explain how the total is derived? Someone at the YMCA this week put this question to me and I gave an answer but I am not sure I am rightso I have come to you. logically it appears 40X40X40=64000. Actually on a standard combination lock it is John Hi John,I agree with your mathematical analysis in both cases, 40x40x40 and 39x39x38, but I am not sure exactly how the combination locks work. My recollection is this: Then you go counterclockwise, past X to Y which can be any number except X. This gives 39 choices. Now go clockwise again to the last number Z which can be any number except Y. This gives 39 choices. I think you need to talk to someone who know how the locks work. Is 0123 a valid combination? is 575 a valid combination? is 555 a valid combination? I don't know. Cheers,Penny
