2022 Canadian Junior Mathematical Olympiad

Part of Canadian Junior Mathematical Olympiad

Subcontests

(2)

1

T shape and square

You have an infinite stack of T-shaped tetrominoes (composed of four squares of side length 1), and an n × n board. You are allowed to place some tetrominoes on the board, possibly rotated, as long as no two tetrominoes overlap and no tetrominoes extend off the board. For which values of n can you cover the entire board?

1

Easy geometry

\triangle{ABC}

has circumcircle

\Gamma

, drop the perpendicular line from

A

BC

\Gamma

D

, similarly, altitude from

B

AC

\Gamma

E

. Prove that if

AB=DE, \angle{ACB}=60^{\circ}

(sorry it is from my memory I can't remember the exact problem, but it means the same)