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Oh guys... I'm in front of an ATM and want to withdraw some money, but I forgot my 4 digit PIN. Can somebody help me out?

I have a backup card with 6x6 fields, each field has exactly one character!

    - A B C D -
    A - 1 1 3 G
    B 9 - 1 2 C
    C 9 1 - 1 D
    D 9 3 6 - -
    - L C M - -

How do I have to use it?

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    $\begingroup$ I think you have a digit typo in the code box. $\endgroup$
    – Nautilus
    Mar 7, 2016 at 3:18
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    $\begingroup$ No digit typo - I checked it many times. But your question leads to 2 points: 1. You are on the right way! 2. The text is important! $\endgroup$
    – Varon
    Mar 7, 2016 at 8:58
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    $\begingroup$ @Varon Ah, so you actually do know the answer! No more money troubles for you :p $\endgroup$
    – nine9
    Mar 7, 2016 at 11:11
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    $\begingroup$ @nine9: I repeated what a passerby said to me. Bad excuse.. I know ;) $\endgroup$
    – Varon
    Mar 7, 2016 at 11:15
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    $\begingroup$ @Varon Make sure to change your pin though! $\endgroup$ Mar 7, 2016 at 13:18

1 Answer 1

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Your pin is

9476

Argument:

- The table lists the four digits (called $A,B,C,D$).
- The upper right triangle lists the digit sums of the greatest common divisors; for instance, the greatest common divisor of $B=4$ and $D=6$ equals $2$.
- The lower left triangle lists the least common multiples modulo $9$; for instance, the least common multiple of $B=4$ and $D=6$ is $12$, which yields $3$ when taken modulo $9$; similarly, the least common multiple of $C=7$ and $D=6$ modulo $9$ yields $6$.

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  • $\begingroup$ Another way is to apply LCM again and again till you get a single digit. The pin is right anyway. $\endgroup$
    – Varon
    Mar 7, 2016 at 17:33

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