Question
Download Solution PDFIf n pigeons are assigned to m pigeonholes then one of the pigeonholes must contain at least ______ pigeons.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Extended Pigeonhole Principal:
It states that if n pigeons are assigned to m pigeonholes ( the number of pigeons is very large than the number of pigeonholes), then one of the pigeonholes must contain at least
Proof: We can prove this by the method of contradiction.
Assume that each pigeonhole does not contain more than [( n - 1 )/m) pigeons. Then, there will be at most
Hence, for given m pigeonholes, one of these must contain at least
Last updated on May 12, 2025
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