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Australian AMC 2021 - Junior Question 23

AMC AUSTRALIA · Australian AMC 2021 - Junior

Question 23

I have a 4 by 4 by 4 cube made up from 64 unit cubes. I paint 3 faces of the larger cube. Then I pull the cube apart. Which of the following could be the number of unit cubes with no paint on them?
  1. 16
  2. 21
  3. 24
  4. 28
  5. 36