Problem 22 · 2024 Math Kangaroo
Stretch
Logic & Word Problems
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There are four bowls of sweets on a table.
The number of sweets in the first bowl equals the number of bowls that hold one sweet.
The number of sweets in the second bowl equals the number of bowls that hold two sweets.
The number of sweets in the third bowl equals the number of bowls that hold three sweets.
The number of sweets in the fourth bowl equals the number of bowls that hold no sweets.
How many sweets are in the bowls altogether?
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Answer: C — 4
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Hint 1 of 2
Each bowl is counting how many bowls hold a certain number of sweets, so the four numbers must describe themselves.
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Hint 2 of 2
Guess that the counts are small and check whether the four sentences all come out true.
Show solution
Approach: find the one self-consistent filling and add it up
- Try the bowls holding 2, 1, 0, 1 sweets and check the four statements.
- Bowls with one sweet: there are 2 (bowls 2 and 4), matching bowl 1; bowls with two sweets: 1 (bowl 1), matching bowl 2; bowls with three sweets: 0, matching bowl 3; bowls with no sweets: 1 (bowl 3), matching bowl 4.
- Every statement checks out, so the total is \(2+1+0+1=4\), answer C.
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