Problem 14 · 2019 Math Kangaroo
Hard
Counting & Probability
careful-countinglogic
Anna, Bella, Claire, Dora and Erika meet at a party. Each pair who know each other shake hands exactly once. Anna shakes hands once, Bella twice, Claire three times and Dora four times. How many people does Erika shake hands with?
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Answer: B — 2
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Hint 1 of 2
Start from Dora, who shook hands four times, so she met everyone else.
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Hint 2 of 2
Peel off who Anna, Bella and Claire could have shaken to find Erika's count.
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Approach: reason from the largest handshake count down
- Dora shook 4 times, so she shook hands with all of Anna, Bella, Claire and Erika.
- Anna shook only once, so Anna's single handshake was with Dora.
- Claire shook three times: with Dora plus two others, which must be Bella and Erika; Bella's two are Dora and Claire.
- So Erika shook hands with Dora and Claire: 2 people.
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