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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
. QEDOffline
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