Problem 1 · 2018 Math Kangaroo
Easy
Counting & Probability
careful-counting
As seen in the diagram, three darts are thrown at nine fixed balloons. If a balloon is hit it bursts and the dart keeps going in the same direction it had before. How many balloons will not be hit by a dart?
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Answer: B — 3
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Hint 1 of 2
Follow each dart's straight line of travel and mark every balloon it passes through, since a burst balloon lets the dart keep going.
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Hint 2 of 2
Count the balloons that lie on no dart's path - those are the ones never hit.
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Approach: trace each dart's straight path and count the balloons it misses
- Each dart flies in a straight line; whenever it meets a balloon, that balloon bursts and the dart continues the same way, so one dart can hit several balloons in its row.
- Trace all three dart lines and shade every balloon that sits on one of those lines.
- The balloons left unshaded are the ones no dart reaches.
- Counting them gives 3 balloons not hit.
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