Problem 14 · 2025 Math Kangaroo
Medium
Logic & Word Problems
careful-countingcasework
An athlete has a collection of 2 gold medals and 5 silver medals. They are numbered in a certain order from 1 to 7. The images show black-and-white pictures of the medals. Each of the six pictures shows exactly one gold medal. What is the sum of the numbers on the two gold medals?
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Answer: C — 9
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Hint 1 of 2
Each of the six pictures shows exactly one of the two gold medals, the rest silver.
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Hint 2 of 2
A number is gold only if it appears as the single gold in some picture; find which two numbers are always the gold one.
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Approach: identify the two consistently-gold numbers
- Each of the six pictures shows exactly one gold medal among the seven, so the gold medal is the single one that looks different in that picture.
- Comparing the pictures, only two of the numbered medals ever play the role of the gold one — those are the two gold medals.
- Adding the numbers on that gold pair gives 9, answer C.
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