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AMO · 2027 · Grades 4-5 · SET 25 - Self-study Question 4

AMO

Question 4

There are 165 unit cubes arranged in 5 square layers with no space between the cubes as shown. The layers are 1 by 1, 3 by 3, 5 by 5, 7 by 7, and 9 by 9. If a sixth layer is placed on the bottom of the arrangement following the pattern, how many unit cubes are completely surrounded by six other unit cubes?

Follow the centred, aligned square-layer arrangement shown; “surrounded” means sharing each of the six faces with a neighbouring cube.

Question illustration

Choose one letter A–E.
  1. 83
  2. 74
  3. 84
  4. 49
  5. 35