MathDB

Making a present

Source: Baltic Way 2008, Problem 12

November 23, 2008

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Problem Statement

In a school class with

3n

children, any two children make a common present to exactly one other child. Prove that for all odd

n

it is possible that the following holds: For any three children

A

B

and

C

in the class, if

A

and

B

make a present to

C

then

A

and

C

make a present to

B