Problem 8 · 2024 Math Kangaroo
Medium
Logic & Word Problems
substitutionsum-constraint
In the table, each shape stands for a different number. The number at the end of each row is the sum of that row, and the number under each column is the sum of that column. What number does the star stand for?
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Answer: C — 3
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Hint 1 of 3
Each shape always means the same number, and a line of shapes adds up to the number at its end.
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Hint 2 of 3
Start with a line that has two of the SAME shape — that makes the shape easy to figure out.
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Hint 3 of 3
Once you know the heart, look at the middle column to find the star.
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Approach: figure out the easy shapes first, then the star
- The left column is two smileys adding to 10, so each smiley is 5 (because 5 and 5 make 10).
- The right column is two hearts adding to 4, so each heart is 2 (because 2 and 2 make 4).
- The middle column is a heart and a star adding to 5; the heart is 2, and 2 plus 3 makes 5, so the star is 3.
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