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 19:04, 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 
.
