MathDB

Bosnia and Herzegovina EGMO TST 2018 Problem 1

Source: Bosnia and Herzegovina EGMO Team Selection Test 2018

September 19, 2018

Productscirclecombinatorics

Problem Statement

a)

Prove that there exists

5

nonnegative real numbers with sum equal to

1

, such that no matter how we arrange them on circle, two neighboring numbers exist with product not less than

\frac{1}{9}

a)

Prove that for every

5

nonnegative real numbers with sum equal to

1

, we can arrange them on circle, such that product of every two neighboring numbers is not greater than

\frac{1}{9}