MathDB

2008 ToT Spring Junior O P3 ten cards with no a, 10 with b ,10 ten with c

Source:

March 7, 2020

combinatorics

Problem Statement

There are ten cards with the number

a

on each, ten with

b

and ten with

c

, where

a, b

and

c

are distinct real numbers. For every five cards, it is possible to add another five cards so that the sum of the numbers on these ten cards is

0

. Prove that one of

a, b

and

c

0