2018 AMC 8 Problem 3
Attempt Problem 3 of the 2018 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2018 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
3.
Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a as a digit (such as ) or is a multiple of that person leaves the circle and the counting continues. Who is the last one present in the circle?
Answer: D
Small hint:
Simulate only the numbers that cause someone to leave.
Big hint:
Keep the counting order after each person leaves; the next number goes to the next person still in the circle.
Video solution:
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Written solution:
The first five removal numbers are Tracking only those turns gives:
Arn says , Cyd says , Fon says , Bob says , and Eve says .
Dan is the only student remaining, so D is the correct answer.
Problem 3 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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