Problem 14 · 2018 Math Kangaroo
Hard
Logic & Word Problems
casework
The two girls Eva and Olga and the three boys Adam, Isaac, and Urban play together with a ball. When a girl has the ball she throws it either to the other girl or to a boy. Every boy throws the ball only to another boy, but never back to the boy it just came from. The first throw is made by Eva to Adam. Who makes the 5th throw?
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Answer: A — Adam
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Hint 1 of 2
After Eva throws to Adam, the ball stays among the three boys, and a boy never throws back to whoever just threw to him.
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Hint 2 of 2
Track who holds the ball before each throw; the no-return rule on three boys forces the 5th thrower.
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Approach: trace the holder, using the no-immediate-return rule
- Throw 1 is Eva to Adam, so Adam makes throw 2.
- From then on the ball moves only among the three boys, each time to a boy other than the one who just passed it.
- On a triangle of three boys this no-return rule sends the ball Adam -> (a boy) -> (the third boy) -> back to Adam.
- So the maker of the 5th throw is Adam.
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