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ASU 272 All Soviet Union MO 1979 list of random numbers, arithmetic mean

Source:

July 14, 2019

combinatoricsarithmetic mean

Problem Statement

Some numbers are written in the notebook. We can add to that list the arithmetic mean of some of them, if it doesn't equal to the number, already having been included in it. Let us start with two numbers,

0

and

1

. Prove that it is possible to obtain :
a)

1/5

,
b) an arbitrary rational number between

0

and

1

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