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2020 Math Kangaroo

Problem 7

Problem 7 · 2020 Math Kangaroo Medium
Spatial & Visual Reasoning cube-viewscareful-counting

Maria made a block using white cubes and coloured cubes in equal amounts. How many of the white cubes cannot be seen in the picture?

Figure for Math Kangaroo 2020 Problem 7
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Answer: B — 2
Show hints
Hint 1 of 2
First count how many small cubes the whole block contains.
Still stuck? Show hint 2 →
Hint 2 of 2
Half are white; subtract the white cubes you can actually see on the surface.
Show solution
Approach: count total, split evenly, then subtract visible whites
  1. The block is made of cubes split equally into white and coloured.
  2. Half of the cubes are white.
  3. Compare that total with the white cubes showing on the visible faces.
  4. The white cubes that must be hidden inside number 2.
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