Questions involving the pigeonhole principle in Combinatorial Analysis.
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Consider a set A of 100, 000 arbitrary integers. Prove that there is some subset of 22 integers that end in the same last three digits.
Consider a set A of 100, 000 arbitrary integers. Prove that there is
some subset of 22 integers that end in the same last three digits.
I'm new to this principle and need help on this problem.
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Another version of PP
Prove the following version of the pigeonhole principle. Let $m$ and $n$ be
positive integers. If $m$ objects are distributed in some way among $n$ containers,
then at least one container must hold at ...
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How small parallelograms are we guaranteed to get, when we select the two sides from different plane lattices?
This a shortened version (motivation from telecommunications stripped away) of a question I asked in MO in late May (no answers). I am mostly checking, if somebody has seen this or a related question ...
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PigeonHole Principle how to apply this?
This problem was suggested to me by one of the students. Imagine you are one
of four players. Each player gets two cards from a regular deck of cards. Your
hand is 10 10. You lose only if some other ...
