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Monday, May 18, 2015

Postal Pigeonholing


To start the week, another thought problem I've adapted again from Posamentier & Krulik's "Problem-solving Strategies in Mathematics." It's actually quite simple, though the language can throw people off:

A certain neighborhood includes 50 condominiums (1 mailbox/household per condominium). One afternoon, the postman has 151 pieces of mail to deliver to those 50 households. What is the largest number of letters that some household is guaranteed to receive?
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Answer:   4
...of course there are many possible (but UNguaranteed) scenarios in which one (or more) of the households could get far more than 4 items, but if we look at the 'most evenly spread out case,' 50 recipients will get 3 items, and there is still one more remaining that must go to someone, who thus ends up with 4; i.e., SOMEone is guaranteed to get at least 4 items.


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