Show that, given any 12 natural numbers, we can choose two of them such that their difference is divisible by 11.

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- Oct 4th 2009, 10:16 AMbillymGiven any 12 natural numbers...
Show that, given any 12 natural numbers, we can choose two of them such that their difference is divisible by 11.

- Oct 4th 2009, 10:24 AMbillym
nevermind i got it. didnt read the question properly (again)

- Oct 4th 2009, 11:50 AMPlato
If two number have the same remainder when divided be eleven then there difference is divisible by eleven. There are only eleven possible remainders, $\displaystyle \{0,1,2,\cdots,9,10\}$, when an integer is divided by eleven.

You have twelve integers. What does that tell you?