MathDB

A subset of

\{1, 2, 3, ... ... , 2015\}

is called good if the following condition is fulfilled: for any element

x

of the subset, the sum of all the other elements in the subset has the same last digit as

x

. For example,

\{10, 20, 30\}

is a good subset since

10

has the same last digit as

20 + 30 = 50

20

has the same last digit as

10 + 30 = 40

, and

30

has the same last digit as

10 + 20 = 30

. (a) Find an example of a good subset with 400 elements. (b) Prove that there is no good subset with 405 elements.

Problem Statement