Problem 16 · 2021 Math Kangaroo
Medium
Spatial & Visual Reasoning
cube-viewscasework
A triangular pyramid is built with 10 identical balls. Each ball has one of the letters A, B, C, D and E on it, and there are 2 balls marked with each letter. The picture shows 3 side views of the pyramid. What is the letter on the ball with the question mark?
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Answer: A — A
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Hint 1 of 2
Ten balls, two of each of A–E; the three side views show different faces of the same pyramid.
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Hint 2 of 2
Use the visible letters to deduce which letters are already placed, leaving the '?' ball's identity.
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Approach: reconcile the three views
- Each letter appears exactly twice among the ten balls, and the three views show the pyramid from different sides.
- Tracking which positions carry which letters across the views fixes every ball except the marked one.
- The leftover letter for the '?' ball is A.
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