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Partitioned into 32 sets of equal size and equal sum

Source: China Girls Math Olympiad 2008, Problem 1

August 26, 2008
combinatorics unsolvedcombinatorics

Problem Statement

(a) Determine if the set {1,2,…,96} \{1,2,\ldots,96\} can be partitioned into 32 sets of equal size and equal sum. (b) Determine if the set {1,2,…,99} \{1,2,\ldots,99\} can be partitioned into 33 sets of equal size and equal sum.
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