1989 AMC 8 Problem 22
Attempt Problem 22 of the 1989 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1989 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
The letters and the digits are each cycled separately (shifted one place at a time) to build a numbered list. Starting from AJHSME the list begins: line is JHSMEA line is HSMEAJ line is SMEAJH and so on. On what numbered line will AJHSME appear for the first time?
Answer: C
Small hint:
The six letters return to AJHSME every lines; the four digits return to every lines
Big hint:
Both return together on the least common multiple of and
Solution:
The six letters cycle back to their original order AJHSME every lines, and the four digits cycle back to every lines.
Both happen on the same line at the least common multiple of and which is So AJHSME first reappears on line
Thus, the correct answer is C .
Problem 22 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
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