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Australian AMC 2010 - Junior Question 24

AMC AUSTRALIA · Australian AMC 2010 - Junior

Question 24

Two mad tilers Arch and Bill are tiling the large foyer of a new building with square tiles. Arch lays the first tile, Bill doubles the area tiled by laying another tile to make a rectangle. Then Arch lays two more tiles to make a square-shaped set of tiles. They keep doubling the area tiled using either a square array of tiles (Arch) or a rectangular array (Bill). At lunchtime they looked at what they had done. Which one of the following statements could be true?
  1. Bill laid the last tile and there are 256 tiles laid.
  2. Arch laid the last tile and there are 2048 tiles laid.
  3. Bill laid the last tile and the overall shape of the tiles is a square.
  4. Bill will lay the next tile after lunch and there are 8192 tiles laid.
  5. Arch will lay the next tile after lunch and there are 512 laid.