MathDB

Find the number of ways to completely cover a

2 \times 10

rectangular grid of unit squares with

2 \times 1

rectangles

R

and

\sqrt{2}

\sqrt{2}

2

triangles

T

such that the following all hold:
[*] a placement of

R

must have all of its sides parallel to the grid lines, [*] a placement of

T

must have its longest side parallel to a grid line, [*] the tiles are non-overlapping, and [*] no tile extends outside the boundary of the grid.
(The figure below shows an example of such a tiling; consider tilings that differ by reflections to be distinct.) [asy] unitsize(1cm); fill((0,0)--(10,0)--(10,2)--(0,2)--cycle, grey); draw((0,0)--(10,0)--(10,2)--(0,2)--cycle); draw((1,0)--(1,2)); draw((1,2)--(3,0)); draw((1,0)--(3,2)); draw((3,2)--(5,0)); draw((3,0)--(5,2)); draw((2,1)--(4,1)); draw((5,0)--(5,2)); draw((7,0)--(7,2)); draw((5,1)--(7,1)); draw((8,0)--(8,2)); draw((8,0)--(10,2)); draw((8,2)--(10,0)); [/asy]

Problem Statement