Problem 23 · 2021 Math Kangaroo
Stretch
Logic & Word Problems
Spatial & Visual Reasoning
careful-countingcasework
A triangular pyramid is built with 20 cannon balls, as shown. Each cannon ball is labelled with one of A, B, C, D or E. There are 4 cannon balls with each type of label. The picture shows the labels on the cannon balls on 3 of the faces of the pyramid. What is the label on the hidden cannon ball in the middle of the fourth face?
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Answer: D — D
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Hint 1 of 2
Each label A–E is used exactly four times across the 20 balls.
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Hint 2 of 2
Tally how many of each label already appear on the three shown faces (counting shared edge balls once); the centre ball must be the label still short of four.
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Approach: count each label and find the one not yet at full quota
- There are 4 balls of each label. Tally the labels visible on the three shown faces, counting shared edge/corner balls once.
- One label falls one short of its quota of 4; that missing ball is the hidden centre of the fourth face.
- That label is D.
- So the answer is D.
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