MathDB

A unit square is removed from the corner of an

n \times n

grid, where

n \geq 2

. Prove that the remainder can be covered by copies of the figures of

3

5

unit squares depicted in the drawing below. [asy] import geometry;
draw((-1.5,0)--(-3.5,0)--(-3.5,2)--(-2.5,2)--(-2.5,1)--(-1.5,1)--cycle); draw((-3.5,1)--(-2.5,1)--(-2.5,0));
draw((0.5,0)--(0.5,3)--(1.5,3)--(1.5,1)--(3.5,1)--(3.5,0)--cycle); draw((1.5,0)--(1.5,1)); draw((2.5,0)--(2.5,1)); draw((0.5,1)--(1.5,1)); draw((0.5,2)--(1.5,2)); [/asy]
Note: Every square must be covered once and figures must not go over the bounds of the grid.

Problem Statement