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| Math Central | Quandaries & Queries |
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Question from Tricia, a parent: I have a bike lock that I know the numbers 3, 6, 8, & 9 are part of the combination, but I can't remember the order. What is the calculation to get all of the possible combinations. |
Hi Tricia.
Just go through them in sequence:
All the possibliities starting with a 3 are:
3689 3698 3869 3896 3968 3986
Likewise,
6389 6398 6839 6893 6938 6983
8369 8396 8639 8693 8936 8963
9368 9386 9638 9683 9836 9863
As you can see, there are 24 in total. This is because there are four choices for the first digit, then once that is chosen, there are three remaining choices for the second digit, then two for the third and whatever is left over must be the fourth digit. So that is four choices times three choices times two choices times one choice. 4 x 3 x 2 x 1 = 24.
Twenty four attempts to open your lock won't take long.
Stephen.
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