Use the Pigeonhole Principle to explain why any collection of 12 positive integers must contain two numbers whos difference is divisible by 10. Your answer should make it clear that you understand what the Pigeonhole Principle says (you may express it informally).
If got a general idea, that since there are 12 numbers, there must be two numbers that add up to form a multiple of ten because there are only 10 single unit digits, and there only needs to be 2 other digits to make a multiple of ten. Example: Take the numbers 1,3,6,10,12,13,18,20,21,22,25, and 27. Here, since 27 and 3 add up to 30, and 30 is divisible by 10... but that wont always work, such as if you take 11,21,31,41,51,61,71,81,91,101,111, and 121.
Help?
2006-10-26
09:12:33
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7 answers
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asked by
azmurath
3
in
Mathematics