GK 2019 Q11
11. Alan, Bella, Claire, Dora, and Erik met together and shook hands exactly once with everyone they already knew. Alan shook hands once, Bella shook hands twice, Claire shook hands three times and Dora shook hands four times. How many times did Erik shake hands?
- A 1
- B 2
- C 3
- D 4
- E 5
Grey Kangaroo 2019, Question 11. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 2
Since Dora shook hands four times, she shook hands with all the other four people. Hence, since Alan only shook hands once, it was with Dora. Since Claire shook hands three times and did not shake hands with Alan, she shook hands with Bella, Dora and Erik. Hence, since Bella only shook hands twice, it was with Dora and Claire. Therefore Erik shook hands twice (with Dora and Claire).
Solution © UK Mathematics Trust, from the GK 2019 solutions.