2022 AMC 12A Problem 7
Attempt Problem 7 of the 2022 AMC 12A 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 2022 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
7.
A rectangle is partitioned into regions as shown. Each region is to be painted a solid color - red, orange, yellow, blue, or green - so that regions that touch are painted different colors, and colors can be used more than once. How many different colorings are possible?
Answer: D
Small hint:
Color the region that borders the most others first
Big hint:
One region touches all four others; each remaining region must avoid two already-used colors
Solution:
The bottom-middle region shares a border with all four other regions. Color it first in ways.
The top-left region borders it, giving choices. Each of the three remaining regions borders exactly two already-colored regions, which have different colors, leaving choices apiece.
The total is
Thus, the correct answer is D.
Problem 7 in other years
- 1950 AMC 12
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