2

Part of 2017 Bosnia and Herzegovina Junior BMO TST

Problems(1)

Bosnia and Herzegovina JBMO TST 2017 Problem 2

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2017

A

A=\{1,2,3,...,2017\}

S

A

is good if for all

x\in A

sum of remaining elements of set

S

has same last digit as

x

. Prove that good subset with

405

elements is not possible.

combinatoricsSetsSubsets