Question: 1. Consider g : {0,9,8,7,6,5}→{4,3,2,1}. Is it possible for g to be one-to one? Onto?
2. Figure shows a 2×4 grid that has been tiled with four 1×2 rectangles.
(a) How many ways are there to tile a 2×1 grid with 1×2 rectangles? (The rectangles may be rotated so as to be 2×1 rectangles.)
(b) How many ways are there to tile a 2×2 grid with 1×2 rectangles?
(c) How many ways are there to tile a 2×3 grid with 1×2 rectangles?
(d) How many ways are there to tile a 2×4 grid with 1×2 rectangles?
(e) How many ways are there to tile a 2× n grid with 1× 2 rectangles? Make and prove a conjecture.
