Problem 24 · 2016 Math Kangaroo
Stretch
Logic & Word Problems
careful-countingcasework
Five sparrows sit on a rope and look in one or the other direction (see picture). Every sparrow whistles as many times as the number of sparrows it can see in front of it, so Azra whistles four times. Then one sparrow turns to face the opposite direction, and again all the sparrows whistle by the same rule. The second time the sparrows whistle more often in total than the first time. Which sparrow turned around?
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Answer: B — Bernhard
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Hint 1 of 3
Each sparrow whistles once for every sparrow it can see in the direction its beak points.
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Hint 2 of 3
A turn raises the total only when the sparrow was looking the 'short' way and now looks toward the bigger group.
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Hint 3 of 3
Look for the sparrow who can see only a few birds now but would see many more after turning.
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Approach: count each sparrow's view, then find the single turn that grows the total
- Count what each bird sees the way it faces: Azra sees 4 ahead, Christa 2, David 3, Elsa 4, while Bernhard is looking back and sees only 1 (just Azra), giving 4 + 1 + 2 + 3 + 4 = 14 whistles.
- Turning a bird helps the total only if it then faces the larger crowd; Azra, Christa, David and Elsa would each end up seeing the same or fewer birds.
- Bernhard is the one looking the short way: turn him around and he now sees the three birds on his other side instead of one, lifting the total to 16.
- So the sparrow that turned around is Bernhard, choice B.
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