Problem 24 · 2013 Math Kangaroo
Stretch
Logic & Word Problems
careful-counting
40 boys and 28 girls hold hands in a big circle. Exactly 18 boys give their right hand to a girl. How many boys give their left hand to a girl?
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Answer: A — 18
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Hint 1 of 3
Each boy-and-girl neighbour pair is one boy's hand joined to one girl's hand.
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Hint 2 of 3
Walk around the circle one way and mark every spot where a boy is followed by a girl, and every spot where a girl is followed by a boy.
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Hint 3 of 3
Since the circle closes up, those two kinds of spots must come in equal numbers.
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Approach: match boy→girl and girl→boy spots around the circle
- Walk around the circle one way. Every place where a boy is followed by a girl is a boy giving that hand to a girl; every place a girl is followed by a boy is a girl giving her hand to a boy.
- Going around a loop, the number of boy→girl spots equals the number of girl→boy spots, because the two kinds must alternate.
- So just as many boys give their left hand to a girl as give their right hand to a girl: 18.
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