Problem 28 · 2016 Math Kangaroo
Stretch
Logic & Word Problems
casework
Four sportswomen and sportsmen are sitting around a round table for dinner. They do four different sports: ice skating, skiing, hockey and sledging. The person who skies sits to the left of Sandra. The person who ice skates sits opposite Benjamin. Eva and Philipp sit next to each other. A woman sits next to the person who plays hockey. Which sport does Eva do?
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Answer: A — Ice skating
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Hint 1 of 3
Note the women are Sandra and Eva; the men are Benjamin and Philipp.
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Hint 2 of 3
Seat Eva and Philipp side by side, then use 'ice skater opposite Benjamin' to test who skates.
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Hint 3 of 3
Finish with 'a woman sits next to the hockey player' to rule out the wrong seating.
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Approach: place the two friends, then test the opposite clue
- Put Eva and Philipp next to each other; the remaining two seats hold Sandra and Benjamin, opposite Eva and Philipp respectively.
- If Benjamin sits opposite Philipp, then the ice skater (opposite Benjamin) is Eva; if Benjamin sits opposite Eva, the skater is Philipp.
- In the second seating the hockey player ends up with only men as neighbours, breaking 'a woman sits next to the hockey player', so that seating is impossible.
- Only the first seating survives, and there the ice skater opposite Benjamin is Eva, so Eva does ice skating.
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