Floor Borders One Foot Wide and of Varying Lengths Are $1 ^ { \prime } \times 3 ^ { \prime }$

Essay

Floor borders one foot wide and of varying lengths are to be covered with nonoverlapping tiles that are available in two sizes: $1 ^ { \prime } \times 3 ^ { \prime }$ and $1 ^ { \prime } \times 5 ^ { \prime }$ sizes. Assuming that the supply of each size is infinite, prove that every $1 ^ { \prime } \times n ^ { \prime }$ border $( n > 7 )$ can be covered with these tiles.