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Problem of the Week 816

Five out of Ten

Given a set X of integers let S(X) be all sums of all 5-element subsets of X.

Are there two sets, X and Y, of ten elements each so that S(X) = S(Y)?

Source: Leningrad Math Olympiad

Bonus: (I don't know the answer to this one). What if 5 is replaced by 2? (but the 10 is retained).

A List of Lists:

The web page "" contains the List of Recreational Mathematics Mailing Lists which is edited by Ivan Skvarca. It includes thirteen lists of recreational mathematics, puzzles, and games, writen in English, Spanish, French, Italian and Portuguese.

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998