![]() ![]() Given that n > m, the principle states that there will always be a pigeonhole with more than 1 pigeon in it. Question: I would like to work on this amazing principle with my students for a week and was, therefore, gathering problems related to the Pigeonhole Principle with beautiful solutions. In this article, we’ll first define what the pigeonhole principle is, followed by some examples to illustrate how it can be applied. Say you have n pigeons, and m pigeonholes. Prove that from a set of ten distinct two-digit numbers (in the decimal system), it is possible to select two disjoint subsets whose members have the same sum.Īt this point, you might have noticed how useful the Pigeonhole Principle can be, if you know how to recognize and use it. ![]() Here's some list of problems that I know (I don't know references at all)Ĭhoose 51 numbers from $\\qquad\square$Īnother problem which can be solved with the Pigeonprinciple is the following: ![]()
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