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The above piece of chocolate looks like a square with 4 pieces stuck on to it. How can you divide it with 4 straight cuts that they may form four congruent squares when moved? (You may not move the pieces until all cuts have been made, and you may not rotate or flip over any of the pieces when moving them. Also, all the chocolate must be used to make the squares.)

This shape tessellates.  If you draw a few copies on a sheet of graph paper you can make your cuts as continuous lines across many copies of the shape.

If these cuts are parallel to lines connecting the centers of neighboring shapes, they will cut all shapes the same.

Note for this shape, the lines connecting neighboring centers have slopes of 1/2 and -2 (or -1/2 and 2)

This is just the slope you need to get sides = ��5

The only thing left is to find four such lines that fit inside one shape.  They are two perpendicular sets.

nikki described the placement of these lines well, I think.

The tesselation shows how the pieces will re-form into squares.

-Jer

(sorry if that made no sense at the end)

Posted by Jer on 2004-10-14 16:15:13