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2021 AMC Fall 10A Problem 24

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2021 AMC Fall 10A Problem 24AMC 10 Step by Step

Name: Date: September 13, 2026

Arrangements with Restrictions · difficulty 4 of 5 · about 10 min · position P21-25

Each of the $12$ edges of a cube is labeled $0$ or $1$ . Two labelings are considered different even if one can be obtained from the other by a sequence of one or more rotations and/or reflections. For how many such labelings is the sum of the labels on the edges of each of the $6$ faces of the cube equal to $2$ ?

A)
$8$
B)
$10$
C)
$12$
D)
$16$
E)
$20$

2021 AMC Fall 10A Problem 24

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