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    alexandrugiurca's Avatar
    alexandrugiurca Posts: 1, Reputation: 1
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    #1

    Feb 27, 2014, 09:48 AM
    100 vertices in a prism with a 50-gon
    There are 100 vertices in a prism with a 50-gon as its base. Those vertices are assigned integers 1 to 100 (inclusive) in a random order. Each number can only be assigned once. The objective is to prove that there are always two adjacent vertices (two vertices that are connected by an edge) whose number differ by 48 or less.

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    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    Feb 27, 2014, 03:07 PM
    Are you sure the problem isn't to show that at least two adjacent sides must differ by 49 or less? Also, what's with the "50-gon" base - to have 100 sides shouldn't it be a "100-gon" base?
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