Math CentralQuandaries & Queries


Question from peggy, a parent:
my son has locked his ipod and can't remember the combo.
He knows it has the numbers 2-5-8 in it but not the fourth number or the order. could you help us?

Hey, I'm a mathematician not a psychic! (Yes, I can prove that. I think, therefore I exist. Psychics don't exist. Therefore I'm not a psychic.) But here are some hints.

  1. He would probably have remembered if he had repeated one of those digits.
    If he agrees that he did not have a repeated digit,
    that rules out some possibilities (there are 7x24 = 168 left.) If he thinks he did, that narrows it down even more to 3x6 = 36. If there isn't a lockout feature, he can try all 204 possibilities in under an hour. He might want to write out a list first.

  2. He may be able to remember something about how he picked the number. I don't have an Ipod myself but I know it uses a "ring" directional controller. Thus, entering numbers is presumably done by moving a cursor over a grid of numbers and clicking on the right ones. "Easy" patterns are ones with a simple geometric shape on the grid.
    For instance, on a touchtone keypad (the most likely layout) 2-5-8 run down the middle. Obvious extensions of these to 4 digits would be:

    2-5-8-0, 2-5-8-7, 2-5-8-9, 1-2-5-8, 3-2-5-8,

    and the same ones backwards. If that doesn't work keep trying the same idea.

Good Hunting!

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