GK 2018 Q11
11. A lion is hidden in one of three rooms. A note on the door of room 1 reads “The lion is here”. A note on the door of room 2 reads “The lion is not here”. A note on the door of room 3 reads “2 + 3 = 2 × 3”. Only one of these notes is true. In which room is the lion hidden?
- A In room 1.
- B In room 2.
- C In room 3.
- D It may be in any room.
- E It may be in either room 1 or room 2.
Grey Kangaroo 2018, Question 11. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C In room 3.
Consider the three possible positions of the lion in turn. If the lion were in room 1, the notes on both room 1 and room 2 would be true. Hence the lion is not in room 1. If the lion were in room 2, the notes on all three rooms would be false. Hence the lion is not in room 2. However, if the lion were in room 3, the notes on room 1 and room 3 would be false but the note on room 2 would be true. Hence the lion is in room 3.
Solution © UK Mathematics Trust, from the GK 2018 solutions.