Problem 2 · 2009 Math Kangaroo
Easy
Counting & Probability
careful-counting
At a party there were 4 boys and 4 girls. Boys only danced with girls and girls only danced with boys. At the end of the evening each person was asked how many people they had danced with. The boys gave the answers 3, 1, 2, 2 and three of the girls answered 2. Which answer did the fourth girl give?
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Answer: C — 2
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Hint 1 of 2
Each dance pairs one boy with one girl, so the boys' counts and the girls' counts add up to the same total.
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Hint 2 of 2
Add the boys' answers, then subtract the three known girls' answers.
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Approach: count each dance from both sides
- Every dance links a boy and a girl, so the sum of the boys' partner-counts equals the sum of the girls'.
- Boys reported 3+1+2+2 = 8 dances in total.
- Three girls reported 2 each = 6, so the fourth girl danced 8-6 = 2 times.
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