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Possible Duplicate:
Chess Master Problem

A child drinks at least 1 bottle of milk a day. Given that he has drunk 700 bottles of milk in a year of 365 days, prove that for he has drunk exactly 29 bottles in some consecutive days.

I think this problem could be solved by the pigeonhole principle but I am not sure.

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    The answer in the dupe essentially works for this. – Aryabhata Apr 16 '12 at 21:43
  • Another answer that also works is the one that I added here: http://math.stackexchange.com/questions/97397/combinatorics-pigeonhole-principle-question. The solution would be very similar to the answer I added there, but I think there is not enough room here in the comments to detail it. Anyway, it starts by building these sets: {1,30,59,...,668,697}; {2,31,60, ...,669,698}; {3,32,61,...,670,699}; {4,33,62, ...,671,700}; ...; {29,58,87,...,696}. There are 29 sets, in total. The first four sets have 25 numbers, and the remaining sets have 24 numbers. The rest of the solution is very similar. – favq Apr 19 '12 at 12:17

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