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2021 AMC Fall 10A Problem 18

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2021 AMC Fall 10A Problem 18AMC 10 Step by Step

Name: Date: September 13, 2026

Arrangements with Restrictions · difficulty 3 of 5 · about 5 min · position P16-20

A farmer's rectangular field is partitioned into $2$ by $2$ grid of $4$ 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?

A)
$12$
B)
$64$
C)
$84$
D)
$90$
E)
$144$

2021 AMC Fall 10A Problem 18

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