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Pandora's Cube

Source: 10B #24/12B #20

November 17, 2021
geometry3D geometryAMCAMC 10AMC 10 BAMC 12AMC 12 B

Problem Statement

A cube is constructed from 44 white unit cubes and 44 black unit cubes. How many different ways are there to construct the 2×2×22 \times 2 \times 2 cube using these smaller cubes? (Two constructions are considered the same if one can be rotated to match the other.)
<spanclass=′latex−bold′>(A)</span> 7<spanclass=′latex−bold′>(B)</span> 8<spanclass=′latex−bold′>(C)</span> 9<spanclass=′latex−bold′>(D)</span> 10<spanclass=′latex−bold′>(E)</span> 11<span class='latex-bold'>(A)</span>\ 7 \qquad<span class='latex-bold'>(B)</span>\ 8 \qquad<span class='latex-bold'>(C)</span>\ 9 \qquad<span class='latex-bold'>(D)</span>\ 10 \qquad<span class='latex-bold'>(E)</span>\ 11
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