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Australian AMC 2011 - Junior Question 24

AMC AUSTRALIA · Australian AMC 2011 - Junior

Question 24

A square-based pyramid is built using cubic blocks, 1 on top, 4 on the next layer, 9 on the next, 16 on the next, and so on.

What is the minimum number of blocks needed if the pyramid is to be dismantled and rebuilt into 2 separate cubes with no blocks left over?
  1. 55
  2. 91
  3. 140
  4. 204
  5. 285