2021 Fall AMC 10A Problems/Problem 18
Problem
A farmer's rectangular field is partitioned into by grid of rectangular sections as shown in the figure. In each section the farmer will plant one crop: corn, wheat, soybeans, or potatoes. The farmer does not want to grow corn and wheat in any two sections that share a border, and the farmer does not want to grow soybeans and potatoes in any two sections that share a border. Given these restrictions, in how many ways can the farmer choose crops to plant in each of the four sections of the field?
Risky, but Quick Solution
The top right box has choices and the top left box has choices. Thus, it is reasonable to assume that the answer is a multiple of . We know that the answer will not be too small or too large, so the answer is
- Aidensharp