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 Cross cut (Posted on 2006-03-06)
I have a cross in the form of one square with four identical squares surrounding it
```   _
_|_|_
|_|_|_|
|_|```
Cut it into the fewest number of pieces possible such that, when rearranged the pieces form two smaller crosses of identical size.

 No Solution Yet Submitted by Sir Percivale Rating: 3.2500 (4 votes)

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 3 Peice Solution... | Comment 10 of 18 |
Ok, I have to blow up the image in order to show my solution (please excuse my lack of artistic presence)

_ _ _
|       |
|       |
_ _ _|_ _ _|_ _ _
|       |       |       |
|       |       |       |
|_ _ _|_ _ _|_ _ _|
|       |
|       |
|_ _ _|

ok, make two vertical cuts through the middle making these shapes:

_       _       _
|  |    | |     | |
|  |    | |     | |
_ _ _|_|    |_|    |_|_ _ _
|       |  |    | |     | |       |
|       |  |    | |     | |       |
|_ _ _|_|    |_|    |_|_ _ _|
|  |     | |    | |
|  |     | |    | |
|_ |    |_|   |_|

I will call them (a), (b), and (c), respectively.

Rotate (b) 90 degrees.
Join (a) and (c) back together with (b), giving you this shape:

_                           _
|  |                        | |
|  |                        | |
_ _ _|_|                        |_|_ _ _
|       |  |_ _ _ _ _ _ _ _ _| |       |
| a    |  |_ _ _ _b_ _ _ _ _| |  c   |
|_ _ _|_|                       |_|_ _ _|
|  |                        | |
|  |                        | |
|_ |                       |_|

The above is two slightly deformed crosses that are mirror-images of eachother:

_
|  |
|  |
_ _ _|_|
|       |  |_ _ _ _ _
|       |  |_ _ _ _ _|
|_ _ _|_|
|  |
|  |
|_ |

The problem says that there must be two crosses of identical size. It says nothing about exact shape or orientation. These crosses are the exact same shape, only one of them is either mirrored or rotated 180 degrees.

 Posted by Stephen on 2006-03-06 22:51:09

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