MathDB

2

Part of 2007 Dutch Mathematical Olympiad

Problems(1)

partition {1, 2, 3, . . . , 32, 33} into 11 subsets of 3, under conditions

Source: Dutch MO 2007 p2

9/1/2019
Is it possible to partition the set A={1,2,3,...,32,33}A = \{1, 2, 3, ... , 32, 33\} into eleven subsets that contain three integers each, such that for every one of these eleven subsets, one of the integers is equal to the sum of the other two? If so, give such a partition, if not, prove that such a partition cannot exist.
partitioncombinatoricsSetsSubsetSum