Problem 15 · 2014 Math Kangaroo
Hard
Logic & Word Problems
caseworkspatial-reasoning
Ingrid has 4 red, 3 blue, 2 green and 1 yellow cube. She uses them to build the object shown. Cubes with the same colour don't touch each other. Which colour is the cube with the question mark?
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Answer: A — red
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Hint 1 of 3
There are 10 cubes and 10 colour-tiles: 4 red, 3 blue, 2 green, 1 yellow.
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Hint 2 of 3
The rule says two cubes of the same colour may never sit next to each other.
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Hint 3 of 3
Red is the most common colour, so the reds have to be spread far apart all over the pile.
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Approach: there are exactly enough cubes for each colour, so the spread-out rule forces the marked cube's colour
- The pile has 10 cubes, and the colours come in just the right amounts: 4 red, 3 blue, 2 green, 1 yellow.
- No two cubes of the same colour may touch, so the 4 reds must be pushed far apart from one another.
- Filling the pile while keeping every colour from touching its twin leaves only one colour that can go in the marked spot.
- That colour is red — choice A.
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