Problem 13 · 2016 Math Kangaroo
Stretch
Counting & Probability
careful-countingcasework
Five sparrows are sitting on a rope (see picture). Some of them are looking to the left, some of them are looking to the right. Every sparrow whistles as many times as the number of sparrows it can see sitting in front of it. For example, the third sparrow whistles exactly twice. How many times do all the sparrows whistle altogether?
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Answer: D — 10
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Hint 1 of 2
Each sparrow only sees the birds in the direction its beak is pointing.
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Hint 2 of 2
Count how many birds are in front of each sparrow, then add all five counts.
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Approach: count each sparrow's forward view and add them up
- Look at which way each beak points, then count the sparrows in front of it.
- From left to right the sparrows look right, left, right, left, right, so they see 4, 1, 2, 3, and 0 birds in front.
- Adding the whistles: 4 + 1 + 2 + 3 + 0 = 10.
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