2022 AMC 12A Problem 7
Problem 7 of 25EasierCombinatorics
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 choices
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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.
Tagged: graph theory · multiplication principle