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2018 preRMO p22, k=sum of no in partition of {1, 2, ..., 20}, good integer

Source:

August 8, 2019
SetsSubsetspartitionsSumcombinatorics

Problem Statement

A positive integer kk is said to be good if there exists a partition of {1,2,3,...,20} \{1, 2, 3,..., 20\} into disjoint proper subsets such that the sum of the numbers in each subset of the partition is kk. How many good numbers are there?
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