2003 AMC 8 Problem 23
Attempt Problem 23 of the 2003 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 2003 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
23.
In the pattern below, the cat moves clockwise through the four squares and the mouse moves counterclockwise through the eight exterior segments of the four squares.
If the pattern is continued, where would the cat and mouse be after the th move?
Answer: A
Small hint:
The cat repeats every moves.
Big hint:
The mouse repeats every moves; use the remainders of
Solution:
The cat’s position repeats every moves, and the mouse’s position repeats every moves.
Since the cat is in the same position as after the rd move: the lower right square.
Since the mouse is in the same position as after the th move: the left side of the lower left square.
Thus, A is the correct answer.
Problem 23 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
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