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Australian AMC 2013 - Upper Primary Question 23

AMC AUSTRALIA · Australian AMC 2013 - Upper Primary

Question 23

Eight $1\times1$ square tiles are laid to form a shape as shown.

Question illustration

Two more $1\times1$ tiles are added, so that at least one side of each new tile is shared with a side of the original shape. Several different perimeter lengths are now possible. What is the sum of the shortest and longest possible perimeters of the modified shape?
  1. 28
  2. 30
  3. 32
  4. 34
  5. 36