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Partition of set {1,2,3,...,3n} into n subsets {a,b,c}

Source: Serbian National Olympiad 2013, Problem 4

April 8, 2013

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Problem Statement

Determine all natural numbers

n

for which there is a partition of

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

n

pairwise disjoint subsets of the form

\{a,b,c\}

, such that numbers

b-a

and

c-b

are different numbers from the set

\{n-1, n, n+1\}