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Regional Olympiad - FBH 2009 Grade 10 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2009

September 28, 2018

Decompositioncombinatorics

Problem Statement

Decomposition of number

n

is showing

n

as a sum of positive integers (not neccessarily distinct). Order of addends is important. For every positive integer

n

show that number of decompositions is

2^{n-1}