# Difference between revisions of "2003 AMC 10A Problems/Problem 8"

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== See Also == | == See Also == | ||

*[[2003 AMC 10A Problems]] | *[[2003 AMC 10A Problems]] | ||

− | *[[2003 AMC 10A Problems/Problem | + | *[[2003 AMC 10A Problems/Problem 7|Previous Problem]] |

− | *[[2003 AMC 10A Problems/Problem | + | *[[2003 AMC 10A Problems/Problem 9|Next Problem]] |

[[Category:Introductory Geometry Problems]] | [[Category:Introductory Geometry Problems]] |

## Revision as of 20:04, 4 November 2006

## Problem

The polygon enclosed by the solid lines in the figure consists of 4 congruent squares joined edge-to-edge. One more congruent square is attached to an edge at one of the nine positions indicated. How many of the nine resulting polygons can be folded to form a cube with one face missing?

## Solution

Let the squares be labeled , , , and .

When the polygon is folded, the "right" edge of square becomes adjacent to the "bottom edge" of square , and the "bottom" edge of square becomes adjacent to the "bottom" edge of square .

So, any "new" square that is attached to those edges will prevent the polygon from becoming a cube with one face missing.

Therefore, squares , , and will prevent the polygon from becoming a cube with one face missing.

Squares , , , , , and will allow the polygon to become a cube with one face missing when folded.

Thus the answer is .