# Given any 12 natural numbers...

• October 4th 2009, 10:16 AM
billym
Given 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.
• October 4th 2009, 10:24 AM
billym
nevermind i got it. didnt read the question properly (again)
• October 4th 2009, 11:50 AM
Plato
Quote:

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

If two number have the same remainder when divided be eleven then there difference is divisible by eleven. There are only eleven possible remainders, $\{0,1,2,\cdots,9,10\}$, when an integer is divided by eleven.
You have twelve integers. What does that tell you?