MathDB

200

Part of 1974 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

7/4/2019
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?
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