## Ken's POTW

Two Dissections
1. You are given two carpets of dimensions 8-by-8 and 6-by-1. Your task is to make a carpet of dimensions 7 by 10. You are only allowed to cut the 8-by-8 carpet into two pieces. How do you make the cut so that the three carpet pieces can be put together to form the required carpet?

2. Four carpet squares, with side-lengths of 12, 8, 4, and 1, have been lined up together in decreasing order, and sewn together to make one carpet piece, with one long side of length 25. Now it is desired to make a square carpet from this new piece by making as few cuts as possible (folding not allowed...). Where should the cuts be made to make a square carpet which uses all of the carpet?

Source: 1. Internet newsgroup rec.puzzles, 2. Richard Brabant, CSU Sacramento

Solution:
1. The following solution was received from Wilfred Theunissen:
 ```_________________ | ___| | ___| | | ___| | ___________ | |________ | |___________| | ___| | | ___| | |___| | |_______________| ``` ``` --> ``` ```_____________________ | ___| | | ___| | | ___|_______ | | |___________| | | ___| | | ___| | |___|_______________| ```

2. The solution below was received from both Bill Chapp and Richard Brabant:
```|<------------ 15 ----------->|
_______________________________  _
|       2       |             |  ^
|_______________|          3  |  |
|_______4_______|________     |  |
|                       |     |  7
|                       |     |  |
|                       |     |  |
|                       |_____|__v_______
|                             |   |     |
|                             |   |     |
|            1                |   |     |
|                             | 2 |     |________
|                             |   |  3          |
|                             |   |             |
|                             |   |_____________|__
|_____________________________|___|______4________|

```
Are there others?
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