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#1 2009-01-27 14:37:19

fusilli_jerry89
Member
Registered: 2006-06-23
Posts: 86

Pretty Hard. Teacher can't even get it.

A wheel of fortune has the integers from 1 to 25 placed on it in a random manner.
Show that regardless of how the numbers are positioned on the wheel, there are three
adjacent numbers whose sum is at least 39.

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#2 2009-01-27 19:03:15

fusilli_jerry89
Member
Registered: 2006-06-23
Posts: 86

Re: Pretty Hard. Teacher can't even get it.

Think I found a solution. Please let me know if it's valid.


First I concluded that the average number would be 13. Hence, the average group of 3 would be 13 times 3 = 39. In order to have an average of 39, either all numbers have to be 13, or at least one group has to add up to over 39.. thus at least 39.

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#3 2009-01-28 02:00:01

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Pretty Hard. Teacher can't even get it.


Suppoe the statement were false. Label the numbers
clockwise. Then you would have




                 



But

So we get the contradiction

. QED

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