Problem 17 · 2019 Math Kangaroo
Stretch
Algebra & Patterns
substitutionsum-constraint
Each shape represents exactly one digit. The sum of the digits in each row is stated on the right hand-side of each row. Which digit does the star stand for?
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Answer: E — 6
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Hint 1 of 2
A row of three identical circles tells you one circle's value right away.
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Hint 2 of 2
Substitute the circle into the other rows to peel out the star and heart.
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Approach: solve the shape values one at a time
- Row of three circles: 3×circle = 12, so circle = 4.
- Top row: circle + star + heart = 15, so star + heart = 11.
- Bottom row: star + heart + heart = 16, so subtracting gives heart = 5 and star = 6.
- The star stands for 6 (E).
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