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5 numbers on blackboard each replaced by x + y - z, can all be equal ?

Source: 2002 Estonia National Olympiad Final Round grade 9 p4

March 16, 2020

combinatorics

Problem Statement

Mary writes

5

numbers on the blackboard. On each step John replaces one of the numbers on the blackboard by the number

x + y - z

, where

x, y

and

z

are three of the four other numbers on the blackboard. Can John make all five numbers on the blackboard equal, regardless of the numbers initially written by Mary?

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