Problem 11 · 2018 Math Kangaroo
Medium
Arithmetic & Operations
careful-counting
The number of spots on each fly agaric (toadstool) shows how many dwarfs fit under it. We can see one side of each toadstool; the other side has the same number of spots. When it rains, 36 dwarfs try to hide under the toadstools. How many dwarfs get wet?
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Answer: E — 6
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Hint 1 of 3
The back of each mushroom has the same spots as the front, so each mushroom really has double what you see.
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Hint 2 of 3
Work out how many dwarfs fit under all the mushrooms together.
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Hint 3 of 3
If there are more dwarfs than spaces, the leftover dwarfs are the ones who get wet.
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Approach: double the spots you can see, total them, then find the leftover dwarfs
- The spots you can see are 4, 3, 5 and 3, which is 15 spots on the fronts. Each mushroom's back matches its front, so double it: there are really 30 spots in all.
- So 30 dwarfs can hide under the mushrooms.
- But 36 dwarfs come to hide, and 36 − 30 = 6 dwarfs have no space, so 6 get wet.
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