Difference between revisions of "Talk:1986 AIME Problems/Problem 12"

(Created page with "The solution written here seems to incorrect. It is proven that indeed there must be subsets with the same sum when <math>S</math> has more than 5 elements. However, it is not...")
 
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The solution written here seems to incorrect. It is proven that indeed there must be subsets with the same sum when <math>S</math> has more than 5 elements. However, it is not proven that these subsets are disjoint, which is required because the problem condition states that "no two <math>\textbf{disjoint}</math> subsets of <math>S</math> have the same sum," not "no two subsets of <math>S</math> have the same sum."
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The solution written here in the AOPS Wiki for this problem seems to incorrect. It is proven that indeed there must be subsets with the same sum when <math>S</math> has more than 5 elements. However, it is not proven that these subsets are disjoint, which is required because the problem condition states that "no two <math>\textbf{disjoint}</math> subsets of <math>S</math> have the same sum," not "no two subsets of <math>S</math> have the same sum."

Latest revision as of 15:02, 23 October 2017

The solution written here in the AOPS Wiki for this problem seems to incorrect. It is proven that indeed there must be subsets with the same sum when $S$ has more than 5 elements. However, it is not proven that these subsets are disjoint, which is required because the problem condition states that "no two $\textbf{disjoint}$ subsets of $S$ have the same sum," not "no two subsets of $S$ have the same sum."

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