1991 AMC 8 Problem 5
Attempt Problem 5 of the 1991 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 1991 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
5.
A “domino” is made up of two small squares:
. Which of the “checkerboards” illustrated below CANNOT be covered exactly and completely by a whole number of non-overlapping dominoes?
Small hint:
Each domino covers exactly two small squares, so focus on how many small squares each board has.
Big hint:
A board can be fully covered only if its total number of squares is even; find the number of squares in each board by multiplying its two dimensions.
Solution:
Every domino covers exactly squares, so any board that is completely covered by non-overlapping dominoes must contain an even number of small squares.
Counting squares: and Only is odd, so that board cannot be covered. (Each of the even boards has a side of even length and is easily tiled with dominoes.)
Thus, the correct answer is B .
Problem 5 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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