Math CentralQuandaries & Queries


Question from Rob, a parent:

I lost the combo to my lock box, I remember 2 of the #'s in the combo are 6, but dont remember which ones.
What are the possible scenarios knowing the above? Thanks!

Hi Rob.

There are four digits on the combo: xxxx.
Two of them are 6s, so they might be in any of the following positions:

In each case, the xx component is any number, but I bet you would have remembered if there were more than 2 sixes, so I think we only need to consider the two digit values that don't have a six in them.

Those are: 00-05,07-15,17-25,27-35,37-45,47-55,57,58,59,70-75,77-86,87-95,97,99. There are 19 eliminated numbers here.

You would probably remember as well if the other two digits were twins too. So we can eliminate 00, 11, 22, ... 99. That's nine more gone.

Thus, you have 100 - 28 = 72 two-digit numbers together with 6 positions for each. That means 6 x 72 = 432 possible combinations.

I'm not going to list them for you, but now you can see how to do it:

For each of the 72 numbers, try the six permutations
(01): 0166,0616,0661,6016,6061,6601
(02): 0266,0626,0662,0626,6062,6602

Good luck!
Stephen La Rocque.

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