OT - Geometry puzzle

[QuikSand]

Since we’ve been on a little roll lately, here’s a new puzzle – not really math, but rather geometry. Yes, it might be somewhat challenging to represent your answers on the board, but some clever us of the “code” tag ought to suffice.

Take the integers from 1 to 10, inclusive. Use these ten numbers to represent the side measurements of five different rectangles. Now take these five rectangles, and assemble them into a perfect square.

There are multiple solutions to this puzzle, which is a beauty. (Maybe you’ll have to do a little math after all, eh?)

[Maple Leafs]

Curse you...

*****@@@@@@
*****@@@@@@
*****@@@@@@
*****####$$
*****####$$
*****####$$
*****####$$
*****####$$
*****####$$
*****####$$
%%%%%%%%%$$

* = 5x10
@ = 6x3
# = 4x7
$ = 2x8
% = 9x1

[VPI97]

  1         10
  _ _ _ _ _ _ _ _ _ _ _
 | |                   | 2
 | |_ _ _ _ _ _ _ _ _ _|
6| |      7      |     |
 | |            4|     |
 | |             |     |
 |_|_ _ _ _ _ _ _|     | 9
 |               |     |
 |               |     |
5|               |     |
 |               |     |
 |_ _ _ _ _ _ _ _|_ _ _|
         8          3

- 4 x 7
- 1 x 6
- 2 x 10
- 3 x 9
- 5 x 8

[johnnyshaka]

Originally posted by Maple Leafs
Curse you...

*****@@@@@@
*****@@@@@@
*****@@@@@@
*****####$$
*****####$$
*****####$$
*****####$$
*****####$$
*****####$$
*****####$$
%%%%%%%%%$$

* = 5x10
@ = 6x3
# = 4x7
$ = 2x8
% = 9x1

Doesn't look like a "perfect" square to me...it must be wrong.

[Maple Leafs]

Originally posted by johnnyshaka
Doesn't look like a "perfect" square to me...it must be wrong.

Damn, should have used m-dashes...

[QuikSand]

Here is another solution… I believe there are four unique solutions to this.

######&&&&&&&
######&&&&&&&
######&&&&&&&
######&&&&&&&
######&&&&&&&
######&&&&&&&
######&&&&&&&
######&&&&&&&
######&&&&&&&
######%%*****
$$$$$$$$*****
$$$$$$$$*****
$$$$$$$$*****

# = 6 x 10
& = 7 x 9
% = 1 x 2
$ = 8 x 3
* = 5 x 4

[VPI97]

Originally posted by QuikSand
Here is another solution…

Crap. I knew there was a 13 x 13 solution that required the 1 x 2 block, but I got distracted by work before I could finish it.

[VPI97]

        7            6
   _ _ _ _ _ _ _ _ _ _ _ _ _
  |             |           |
 3|             |           | 4
  |_ _ _ _ _ _2_|           |
  |        1|_ _|_ _ _ _ _ _|
  |         |               |
  |         |               |
  |         |               |
10|         |               |
  |         |               | 9
  |         |               |
  |         |               |
  |         |               |
  |_ _ _ _ _|_ _ _ _ _ _ _ _|
       5            8

- 1 x 2
- 3 x 7
- 4 x 6
- 5 x 10
- 8 x 9