Problem 12 · 2019 Math Kangaroo
Medium
Logic & Word Problems
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Anna, Bella, Claire, Dora, Erika and Frieda meet at a party. Each pair who know each other shake hands exactly once. Anna shakes hands only once, Bella twice, Claire three times, Dora four times and Erika five times. How many people does Frieda shake hands with?
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Answer: C — 3
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Hint 1 of 2
Erika shook hands 5 times, so she shook everyone — including Anna, whose single handshake is therefore with Erika.
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Hint 2 of 2
Peel the people off one at a time (Erika, then Dora, …) to see who is left for Frieda.
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Approach: deduce each person's partners step by step
- Erika (5) shook everyone; Anna (1) then only shook Erika.
- Dora (4) shook everyone but Anna: Erika, Bella, Claire, Frieda — giving Bella her 2nd handshake.
- Claire (3) shook Erika, Dora and Frieda, so Frieda's partners are Erika, Dora, Claire: 3 people.
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