MathDB

sums a + b,b + c and a + b + c are nonnegative, numbers around a circle

Source: 2003 Romania JBMO TST 2.3

June 1, 2020

combinatorics

Problem Statement

Five real numbers of absolute values not greater than

1

and having the sum equal to

1

are written on the circumference of a circle. Prove that one can choose three consecutively disposed numbers

a, b, c

, such that all the sums

a + b,b + c

and

a + b + c

are nonnegative.