MathDB

Kilua and Ndoti play the following game in a square

ABCD

: Kilua chooses one of the sides of the square and draws a point

X

at this side. Ndoti chooses one of the other three sides and draws a point Y. Kilua chooses another side that hasn't been chosen and draws a point Z. Finally, Ndoti chooses the last side that hasn't been chosen yet and draws a point W. Each one of the players can draw his point at a vertex of

ABCD

, but they have to choose the side of the square that is going to be used to do that. For example, if Kilua chooses

AB

, he can draws

X

at the point

B

and it doesn't impede Ndoti of choosing

BC

. A vertex cannot de chosen twice. Kilua wins if the area of the convex quadrilateral formed by

X

Y

Z

, and

W

is greater or equal than a half of the area of

ABCD

. Otherwise, Ndoti wins. Which player has a winning strategy? How can he play?

Problem Statement