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 No Rotation Dissection (Posted on 2004-10-19)
Take a square and cut it as you wish into a finite number of pieces. Rearrange the pieces without rotating or flipping any of them to form an new square that is rotated 45-degrees compared to the original.

 No Solution Yet Submitted by Brian Smith Rating: 3.3333 (9 votes)

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 OK, here goes nothing. | Comment 8 of 25 |
you may need to draw this out.
start with a square were the sides are vertical
first cut the corners off at 45degs to the centre of each side.
number the corners CW 1-4 starting in the top left.
now rearrange so 1 is below 4, 3 is left of 4 and 2 is left of 1.

you should now have two squares exactly the same in size and shape.

on the original remaining square make Tic-tac-toe grid to break it up into 9 equal squares, in 5 rows,(it's still at 45degress remember)
with 5 of these squares you need to draw a line at 45degrees (/) to make to rectangles the same size. in the other 4, draw the line the other way (\).

you now have 18 rectangles. 10 going from bottom left to top right(A), and 8 going from top left to bottom right,(B)

take the group of 8(B's) and arrange them long side to the new square, 4 on the top right face, and 4 on the bottom left face.

take the final group of 10 rectangles and arrange them long side to the new "Square"(now rectangle) 5 on the top right and 5 on the bottom left

I think this will suffice.

 Posted by Juggler on 2004-10-19 23:37:39
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