MathDB

min of max {xy, (x- 1)(y - 1), x + y - 2xy} for 0 <= x, y <= 1

Source: 2022 Dutch IMO TST 1.3

December 3, 2022

algebrainequalities

Problem Statement

For real numbers

x

and

y

we define

M(x, y)

to be the maximum of the three numbers

xy

(x- 1)(y - 1)

, and

x + y - 2xy

. Determine the smallest possible value of

M(x, y)

where

x

and

y

range over all real numbers satisfying

0 \le x, y \le 1