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:	post by Man_of_the_Century at 2006-06-26 11:13:05

I found an answer (its not mine, I take no credit):

"With there only being 2k numbers to select from and you have to select half of the numbers plus one, the smaller the k the easier to prove. if you have k = 4, annd you are selecting 5 numbers, start with 5,6,7,8 and that leaves 1 number left to select, with the remaining numbers being 1,2,3,4 which all of these numbers are multiples of one or more of the first numbers. if taking all odd numbers, you have 1 as one of your numbers which make it a multiple of all numbers already chosen. if you take all evens then you would have 2 which is a multiple of all numbers chosen. Its the +1 that makes you have at least two numbers, x and y that are multiples of each other. "

"Your assumption that two people don't shake hands more than once is your proof. Two people in any group K will have shook the same number of hands because two people have only shook hands once."

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