PK 2016 Q23
23. Two sportsmen (Ben and Filip) and two sportswomen (Eva and Andrea) − a speed skater, a skier, a hockey player and a snowboarder − had dinner at a square table, with one person on each edge of the square. The skier sat at Andrea's left hand. The speed skater sat opposite Ben. Eva and Filip sat next to each other. A woman sat at the hockey player's left hand. Which sport did Eva do?
- A speed skating
- B skiing
- C hockey
- D snowboarding
- E more information required
Pink Kangaroo 2016, Question 23. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A speed skating
Put Andrea at the top of the table. Since Eva and Filip are next to each other, Ben must be next to Andrea. If Ben was to her right then he would be opposite the skier, whom we know is to her left. But Ben is opposite the speed skater. So Ben is to Andrea's left and he is the skier. We are now at the stage shown on the diagram.
The hockey player is not opposite Ben, but has a woman to the left. Therefore the hockey player must be at the bottom of the table and Eva is on the left side of the table. So Eva is the speed skater.
Solution © UK Mathematics Trust, from the PK 2016 solutions.