discrete math help!!!?

the intergers 1-10 inclusive are placed around a circle in a random order...show that whatever the order there are always 3 consecutive numbers whose sum is at least 17

i think its the pigeonhole principle but i don't know how to do it

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  • 1 decade ago
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    The sum of all 3 consecutive numbers is

    3(1+2+3+...+10)=165

    Since there are 10 different 3 consecutive numbers, if each of them were at most 16, then the sum of all 3 consecutive numbers would be at most

    10*16=160

    Since this is lower than the sum that we're supposed to get, there must be at least one(rather more than one) 3 consecutive numbers whose sum is at least 17.

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