PK 2015 Q10
10. Three inhabitants of the planet Zog met in a crater and counted each other's ears. Imi said, “I can see exactly 8 ears”; Dimi said, “I can see exactly 7 ears”; Timi said, “I can see exactly 5 ears”. None of them could see their own ears. How many ears does Timi have?
- A 2
- B 4
- C 5
- D 6
- E 7
Pink Kangaroo 2015, Question 10. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 5
The aliens say they can see 8, 7, 5 ears respectively, but each ear has been seen by two aliens so is counted twice. Hence the total number of ears is \(\tfrac{1}{2}(8 + 7 + 5) = 10\) ears. Each alien can see all ten ears, except its own. Timi sees 5 ears, so has \(10 - 5 = 5\) ears.
Solution © UK Mathematics Trust, from the PK 2015 solutions.