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Math olympiad problem |
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| May17-05, 10:56 PM | #1 |
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Math olympiad problem
i have 69 distinct positive whole numbers between 1 and 100. i pick out 4 integers a,b,c,d. prove that i can always pick out 4 integers such that a+b+c=d. can this always hold true with 68 positive integers?
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| May17-05, 11:09 PM | #2 |
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i'm assuming that you don't have to pick out a+b+c=d all the time but there exists a quadruple in your set of 69.
The proof relies on teh pigeon hole principle: [1]let a and d be the smallest and largest of your set of 69 respectively. [2]find the number of pairs taht b & c can be within 1-100 and the set of 69. [3]Compare these two values. |
| May18-05, 09:48 PM | #3 |
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thanks! I seem to know what to do now. The fun part about this problem is the pigeon hole principle. I love math problems like this one.
one of my favorite math problems (though simple) is this: Prove that at any party, two friends at that party must have the same amount of friends present there (given ofcourse that if someone is a friend to you, you are friend to that someone). |
| May18-05, 11:22 PM | #4 |
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Math olympiad problem
if you need a good book to further your proving skillz pick up
"problem solving" by Larson. |
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