Problem 17 · 2024 Math Kangaroo
Hard
Counting & Probability
careful-counting
The digits 0–9 can be drawn using horizontal and vertical lines, as shown. Greg chooses two digits. Together, his digits have 1 horizontal line and 5 vertical lines. What is the sum of his two digits?
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Answer: A — 5
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Hint 1 of 2
Count, for each digit drawn with segments, how many horizontal and how many vertical strokes it uses.
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Hint 2 of 2
Find two digits whose horizontal counts add to 1 and vertical counts add to 5.
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Approach: match segment counts to the required totals
- The digit 1 uses 2 vertical and 0 horizontal segments.
- The digit 4 uses 3 vertical and 1 horizontal segment.
- Together: 2 + 3 = 5 vertical and 0 + 1 = 1 horizontal, exactly as required.
- Their sum is 1 + 4 = 5.
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