Question 22
C2 (CAN). (a) If a $5\times n$ rectangle can be tiled using $n$ pieces like those shown in the diagram, prove that $n$ is even.
(b) Show that there are more than $2\cdot3^{k-1}$ ways to tile a fixed $5\times2k$ rectangle ($k\ge3$) with $2k$ pieces. (Symmetric constructions are considered to be different.)
(b) Show that there are more than $2\cdot3^{k-1}$ ways to tile a fixed $5\times2k$ rectangle ($k\ge3$) with $2k$ pieces. (Symmetric constructions are considered to be different.)