Problem 26 · 2019 Math Kangaroo
Stretch
Number Theory
place-valuecareful-counting
The integers from 1 to 99 are written down in ascending order without a gap. This sequence of digits is divided up into triples (groups of three):
\(123456789101112\cdots979899 \longrightarrow (123)(456)(789)(101)(112)\cdots(979)(899).\)
Which of the following triples is not obtained?
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Answer: B — (444)
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Hint 1 of 2
Write 1234567891011… and chop into groups of three; track where each number lands.
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Hint 2 of 2
Check each candidate triple against the actual grouping — one never appears.
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Approach: generate the triples and check membership
- Concatenate 1 to 99 and split into threes; this gives a fixed list of triples.
- Scanning it, (123), (464), (646) and (888) all occur as groups.
- The triple (444) never lines up, so the answer is (444).
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