Floor borders one foot wide and of varying lengths are to be covered with nonoverlapping tiles that are available in two sizes: $1 ^ { \prime } \times 3 ^ { \prime } \text { and } 1 ^ { \prime } \times 5 ^ { \prime }$ 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.

Question

Floor borders one foot wide and of varying lengths are to be covered with nonoverlapping tiles that are available in two sizes: $1 ^ { \prime } \times 3 ^ { \prime } \text { and } 1 ^ { \prime } \times 5 ^ { \prime }$ 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.

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The Answer of Floor borders one foot wide and of varying lengths are to be covered with nonoverlapping tiles that are available in two sizes: $1 ^ { \prime } \times 3 ^ { \prime } \text { and } 1 ^ { \prime } \times 5 ^ { \prime }$ 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.

Floor Borders One Foot Wide and of Varying Lengths Are 1′×3′ and 1′×5′1 ^ { \prime } \times 3 ^ { \prime } \text { and } 1 ^ { \prime } \times 5 ^ { \prime }1′×3′ and 1′×5′

Floor Borders One Foot Wide and of Varying Lengths Are $1 ^ { \prime } \times 3 ^ { \prime } \text { and } 1 ^ { \prime } \times 5 ^ { \prime }$