Nov 21, 2009

Splitting Problem

How do you cut a rectangular cake into two equal pieces with one straight cut when someone has already removed a rectangular piece from it? (The removed piece can be of any size or any orientation.)

consider these images:

1. What do u mean by "Equal Piece". is it "Equal in Size(area)" or "Symmetric in Shape"

2. You can cut the cake horizontally from the middle. Then both pieces will be the same, in shape and area and volume.

3. A cut through the center of a rectangle divides it in two parts of equal area. In our case, it is sufficient to draw the line that passes through the centers of the two rectangles. Then each will be split in two equal parts.

By the way, the horizontal line considered by KT above, is of course the wrong answer: It might miss altogether the small rectangle.

ML

4. Anonymous, I think KT was thinking of cutting through a plane parallel to the table, from the middle of the cake's height. The images show only the cake's length and width. Assuming the cake is missing a slice, rather than just a chunk, it works. Or at least, it separates the cake in two pieces of equal volume.

By the way, you omitted the case when the two centers coincide and a line isn't defined but I'm nitpicking (and it's got a trivial solution).

5. i think we should find center of mass/gravity of the given piece.
any line passing through center of mass will be our answer because it will divide cake in equal mass, area, volume..

6. Eat all but a 2 by 2 inch square of the cake, then cut that in half.