Problem 8 · 2024 Math Kangaroo
Easy
Number Theory
place-valuecareful-counting
213, 214 and 215 are three numbers in a row, each one more than the one before. Mohammad writes three numbers like that, but with four digits each. His sister erases some digits from each number, leaving:
???7, ?898, 48??
Which digits (from left to right) are missing?
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Answer: D — 4 8 9, 4, 9 9
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Hint 1 of 2
The three numbers are consecutive, and the middle one looks like _898.
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Hint 2 of 2
Pick the four-digit number ending 898, then write the one before and the one after it.
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Approach: identify three consecutive numbers from the visible digits
- The middle number is 4898 (form _898, and it sits between numbers ending 7 and starting 48).
- So the three are 4897, 4898, 4899.
- Filling the gaps: 4897 needs 489, 4898 needs 4, 4899 needs 99.
- Missing digits left to right: 4 8 9, 4, 9 9 — option D.
Mark:
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