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The problem is as follow:

(Thanks to this question for original problem statement)

A row of houses are randomly assigned distinct numbers between 1 and 50 (inclusive). How many houses must there be to insure that there are 5 houses numbered consecutively?

The solution:

Split the numbers into 10 pigeonholes: 1-5, 6-10, 11-15, 16-20… There must be at least =41 “pigeons”=houses

However, I don’t understand how this can be as we could randomly select house numbers like:

1,3,5,7,9,2,4,6,8,10,12,14,16,18,20,11,13, …, 50

So there are no any consecutive numbered houses if we pick numbers like this.

Could someone please explain what I’m missing here?

JoeA
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    They probably mean that the random list must be strictly increasing (as they would be if you were assigning house numbers on a street going from North to South.) – WW1 Feb 14 '23 at 20:35

1 Answers1

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The problem is very badly formulated. It doesn’t mean that there have to be five physically consecutive houses with consecutive numbers; just that there must be some five houses (not necessarily adjacent to each other) that have five consecutive numbers.

joriki
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