1985 AJHSME Problems/Problem 11

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Problem

A piece of paper containing six joined squares labeled as shown in the diagram is folded along the edges of the squares to form a cube. The label of the face opposite the face labeled $\text{X}$ is

$\text{(A)}\ \text{Z} \qquad \text{(B)}\ \text{U} \qquad \text{(C)}\ \text{V} \qquad \text{(D)}\ \ \text{Y} \qquad \text{(E)}\...$

Solution

To find the face opposite $\text{X}$ , we can find the faces sharing an edge with $\text{X}$ , so the only face remaining will be the opposite face.

Clearly, $\text{V}$ and $\text{Z}$ share an edge with $\text{X}$ . Also, the faces $\text{V}$ , $\text{X}$ , and $\text{W}$ share a common vertex, therefore $\text{X}$ shares an edge with $\text{W}$ . Similarly, the faces $\text{U}$ , $\text{V}$ , and $\text{X}$ share a common vertex, so $\text{X}$ shares an edge with $\text{W}$ .

The only face $\text{X}$ doesn't share an edge with is $\text{Y}$ , which is choice $\boxed{\text{D}}$

1985 AJHSME (Problems • Resources)
Preceded by Problem 10	Followed by Problem 12
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

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1985 AJHSME Problems/Problem 11

From AoPSWiki

Problem

Solution

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