MathDB

065

Part of 1965 All Russian Mathematical Olympiad

Problems(1)

ASU 065 All Russian MO 1965 quasi-rounding n numbers

Source:

6/19/2019
Quasi-rounding is a substitution one of the two closest integers instead of the given number. Given nn numbers. Prove that you can quasi-round them in such a way, that a sum of every subset of quasi-rounded numbers will deviate from the sum of the same subset of initial numbers not greater than (n+1)/4(n+1)/4 .
combinatoricsalgebra