Difference between revisions of "2003 AMC 10A Problems/Problem 10"
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Revision as of 19:09, 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 .