MathDB
ASU 200 All Soviet Union MO 1974 every couple of no.s not equal their mean

Source:

July 4, 2019
algebracombinatorics

Problem Statement

a) Prove that you can rearrange the numbers 1,2,...,321, 2, ... , 32 in such a way, that for every couple of numbers none of the numbers between them will equal their arithmetic mean.
b) Can you rearrange the numbers 1,2,...,1001, 2, ... , 100 in such a way, that for every couple of numbers none of the numbers between them will equal their arithmetic mean?
Back to ProblemsView on AoPS