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2025 Math Kangaroo

Problem 3

Problem 3 · 2025 Math Kangaroo Easy
Counting & Probability careful-counting

How many pencils are in this picture?

Figure for Math Kangaroo 2025 Problem 3
Show answer
Answer: B — 8
Show hints
Hint 1 of 3
The pencils cross over each other, so counting the middles is tricky.
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Hint 2 of 3
Each pencil has one pointy tip and one pink eraser end — count the ends instead.
Still stuck? Show hint 3 →
Hint 3 of 3
Count just the pointy tips, or just the pink ends, and that is how many pencils there are.
Show solution
Approach: count by matching each tip to its eraser end
  1. The pencils overlap, so count the ends instead of the middles.
  2. Match each sharpened dark tip to one pink eraser end.
  3. There are 8 such pairs, so there are 8 pencils.
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