Problem 14 · 2018 Math Kangaroo
Medium
Logic & Word Problems
casework
A lion hides in one of three rooms. The note on room 1 reads “The lion is here.” The note on room 2 reads “The lion is not here.” The note on room 3 reads “\(2 + 3 = 2 \times 3\).” Exactly one of the three notes is true. Which room is the lion in?
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Answer: C — Room 3
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Hint 1 of 2
The note on room 3 says 2 + 3 = 2 × 3, i.e. 5 = 6 — is that ever true?
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Hint 2 of 2
Since that note is false, exactly one of the other two notes must be true; test each room.
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Approach: use that exactly one note is true
- Room 3's note (5 = 6) is false, so the single true note is on room 1 or room 2.
- If the lion were in room 1 both notes 1 and 2 would be true; if in room 2 neither would be true.
- If the lion is in room 3, only note 2 ('not here') is true — exactly one. So the lion is in Room 3.
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