Problem 24 · 2025 Math Kangaroo
Stretch
Logic & Word Problems
balance-scalecasework
To compare the weights of a red square, a star and a green circle, Mona uses a beam balance (see picture). The lower pan holds the heavier side. Each shape always has the same weight, different shapes have different weights, and every weight is 1, 2, 3, 4 or 5 kg. How many kilograms does the red square weigh?
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Answer: C — 3 kg
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Hint 1 of 2
The lower pan is heavier: one square outweighs two stars, and two circles outweigh three squares.
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Hint 2 of 2
Try weights 1 to 5 for the square: it must be more than two stars yet light enough that two circles beat three of it.
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Approach: read both balances, then test the square's weight
- Left balance: the square pan is lower, so one square is heavier than two stars.
- Right balance: the two-circle pan is lower, so two circles are heavier than three squares.
- One square beating two stars means the square is at least 3 (two different weights of 1 and 2 already make 3).
- If the square is 4, three squares weigh 12, but two circles can be at most 2×5 = 10 - too light. So the square is 3, with stars 1 and circles 5: 3 > 2 and 10 > 9 both hold, giving 3 kg, option C.
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