MathDB

2

-by-

2018

grid is completely covered by non-overlapping L-tiles (see diagram below) and

1

-by-

1

squares. If the L-tiles can be rotated and flipped, there are a total of

M

such tilings. [asy] size(1cm); draw((0,0)--(2,0)--(2,1)--(1,1)--(1,2)--(0,2)--cycle); draw((0,1)--(1,1)--(1,0)); [/asy] What is

\ln M?

Give your answer as an integer or decimal. If your answer is

A

and the correct answer is

C

, then your score will be

\max\{\lfloor7.5-\tfrac{|A-C|^{1.5}}{20}\rfloor,0\}.

Problem Statement