- #26

- 664

- 3

Sure they can. It's just that end up with a stupid solution. What you MEANT is probably one of:I asserted that the cuts can end in EACH OTHER, which is what you're proposing. But no ONE cut can both start AND end at an edge.

- you forgot to stipulate that both cuts must be a necessary part of the solution.

OR

- *both* cuts cannot start AND end on edges.

Otherwise, imagine the following:

Code:

```
Cake with piece cut out:
+---------------------------------+
| |
| +-----+ |
| | | |
| +-----+ |
| |
| |
| |
| |
| |
| |
+---------------------------------+
Cut number 1:
+---------------------------------+
| |
| +-----+ |
| | | |
| +-----+ |
| |
| ,---+
| ,' |
| --, | |
| `--' |
| |
+---------------------------------+
Cut number 2:
+----------------+----------------+
| | |
| +--+--+ |
| | | |
| +--+--+ |
| | |
| | ,---+
| | ,' |
| | --, | |
| | `--' |
| | |
+----------------+----------------+
```

---------------

A rectangle R exists. A smaller rectangle, P is completely contained within R. All of the edges of P are parallel to the edges of R. None of the edges of P overlap the edges of R. Shape K is defined as the subtraction of P from R.

Two straight line segments, C1 and C2 shall be made. These line segments may result in dividing K into multiple subsequent polygons. Devise a method for placing C1 and C2 such that the sum of the areas of some of the resulting polygons is exactly half of the original area of K.

Restrictions: At least one of C1's endpoints must be an already existing endpoint of one of the edges of K. C1 may be drawn parallel to an existing edge. If C1 is not drawn parallel to an existing edge, then both of its endpoints must be already existing endpoints on the edges of K.

Similarly, at least one of C2's endpoints must be an already existing endpoint of one of the edges of K, or the intersection of C1 and an existing edge. C2 may be drawn parallel to an existing edge of K, or parallel or perpendicular to C1. If C2 is not drawn parallel to an existing edge, or parallel or perpendicular to C1, then both of its endpoints must be already existing endpoints on the edges of K, or the intersections of C1 and an existing edge.

--------------------

That's what I'm assuming the question is asking. Otherwise, I can probably invent a slew of practical answers that are effectively cheats.

DaveE