Problem 13 · 2024 Math Kangaroo
Hard
Logic & Word Problems
substitutionsum-constraint
Zoran builds towers from three different building blocks (a triangle top, a rectangle, and an hourglass). The picture shows the heights of three towers. How high is the fourth tower?
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Answer: A — 12
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Hint 1 of 3
Each kind of block is always the same height, so the same block is worth the same number every time.
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Hint 2 of 3
Compare two towers that are almost the same — the difference in their heights tells you how tall the extra block is.
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Hint 3 of 3
Find the rectangle and the triangle heights, since the fourth tower is just those two stacked.
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Approach: compare towers to find each block's height
- The tall tower (triangle + rectangle + hourglass) is 20, and the short one with just (triangle + hourglass) is 13; the only extra block is the rectangle, so the rectangle is 20 − 13 = 7.
- The tower with (rectangle + hourglass) is 15, and the rectangle is 7, so the hourglass is 8; then in the tower of 13 the triangle is 13 − 8 = 5.
- The fourth tower is just triangle + rectangle = 5 + 7 = 12.
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