MathDB

1

Part of 2023 Malaysian IMO Training Camp

Problems(2)

Matcha Sweep Game

Source: Malaysian IMO TST 2023 P1

4/29/2023
Let PP be a cyclic polygon with circumcenter OO that does not lie on any diagonal, and let SS be the set of points on 2D plane containing PP and OO.
The <spanclass=′latex−italic′>MatchaSweepGame</span><span class='latex-italic'>Matcha Sweep Game</span> is a game between two players AA and BB, with AA going first, such that each choosing a nonempty subset TT of points in SS that has not been previously chosen, and such that if TT has at least 33 vertices then TT forms a convex polygon. The game ends with all points have been chosen, with the player picking the last point wins.
For which polygons PP can AA guarantee a win?
Proposed by Anzo Teh Zhao Yang
combinatorics
Avoid L-triominos

Source: Own. Malaysian SST 2023 P1

8/30/2023
Ivan has a m×nm \times n board, and he color some squares black, so that no three black squares form a L-triomino up to rotations and reflections. What is the maximal number of black squares that Ivan can color?
Proposed by Ivan Chan Kai Chin
combinatorics