22

Part of 2018 India PRMO

Problems(1)

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

Source:

A positive integer

k

is said to be good if there exists a partition of

\{1, 2, 3,..., 20\}

into disjoint proper subsets such that the sum of the numbers in each subset of the partition is

k

. How many good numbers are there?

SetsSubsetspartitionsSumcombinatorics