MAT 300 Spring 04
Dr. Zandieh
Homework #7
Due April 1, 2004
Part I: Recall the “L” shaped tiling of a checker board with a single square tile on one
square from the board. Prove that if a 2n by 2n board has one square covered then the
remaining board can be tiled with “L” shaped pieces. Remember that the “L” shaped
pieces are made of 3 squares.
Part II: Consider a Triangular Board, T(n), made up of equilateral triangles with side
length 1 and 2n triangles on each side. A triangular triomino is a piece made up of three
triangles.
Triangular
Triomino
T(1)
T(2)
T
(
3
)
Prove: For any natural number n ≥ 1, if any corner triangle is removed from T(n) then
the remaining board can be tiled with triangular triominos.
Part III: Consider checkboards with dimensions 2 x 2n and the checkboard is made up of
squares which are alternating colors, red and black. Prove that if one black and one red
square are each covered by a single square tile on any 2 x 2n board of this type, then it
can be tiled by rectangular dominoes of size 2 x 1.