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I've got a digital lock, that I can not unlock. The combination numbers are $2, 6, 8$, and one of them repeat in a $4$ digits sequence. Where can I get a list of all the possible combinations, or any kind of help?

Winther
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Jorge Bruto
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  • How is this a question for real analysis? – David Kraemer Sep 30 '15 at 18:40
  • I just had this question about my dead gran father valt, that no one can open, has I had the numbers and had already make some calculations and failed, I'm just trying to get some help and end up here. – Jorge Bruto Sep 30 '15 at 18:45

1 Answers1

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Suppose it's the $2$ that repeats. You are looking at all permutations of

$2268$. These are exactly $\frac{4!}{2!} = 12$

Same reasoning with $6$ and $8$, and in total there are $36$ such combinations.

Should not be a problem to enumerate them all with paper and pencil ;-)

Edit

To "algorithmically" enumerate all the possibilities, star with

$$2268$$. Now change the order of the last two to get

$$2286$$.

Now put the second digit to be $8$, and to it the same again

$$2826$$$$2862$$ Now the second digit is $6$ and get $$2682$$$$2628$$

Now the first is $8$ and the second $6$

$$8622$$ first $8$, second $2$ $$8262$$$$8226$$

first $6$, second $8$ $$6822$$ first $6$, second $2$

$$6228$$$$6282$$

In total $12$ as expected. Now do the same thing with the other two cases ;-)

Ant
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