MathDB

Let

n

be a positive integer. An equilateral triangle with side

n

will be denoted by

T_n

and is divided in

n^2

unit equilateral triangles with sides parallel to the initial, forming a grid. We will call "trapezoid" the trapezoid which is formed by three equilateral triangles (one base is equal to one and the other is equal to two). Let also

m

be a positive integer with

m<n

and suppose that

T_n

and

T_m

can be tiled with "trapezoids". Prove that, if from

T_n

we remove a

T_m

with the same orientation, then the rest can be tiled with "trapezoids".

Problem Statement