# Puzzling Rectangle

Download the PDF to print out the puzzle. (each unit is 0.19 inches) Dropbox File

There are 12 total pieces: (by order of increasing area)

• 4 x 14
• 7 x 10
• 6 x 28
• 7 x 28
• 14 x 17
• 14 x 21
• 14 x 21
• 10 x 32
• 11 x 32
• 18 x 21
• 18 x 21
• 14 x 28

The challenge of this puzzle is to arrange the pieces in such a way that, together, they create a rectangle. There can be no pieces left out, and no gaps within the rectangle.

My challenge to you is to mathematically prove the number of possible solutions and/or find all of the possible dimensions of the solution.

If anyone is bold enough to tackle this challenge, try and solve the puzzle. This can be done physically using the pieces provided above, or mathematically. Both ways are incredibly hard, so I wish any of you brave enough to take on this challenge good luck.

This puzzle is also a great coffee table puzzle. You can recreate the pieces in wood if you are able to, or print the pieces on cardstock to make them more durable. Challenge friends or family to form a rectangle using all of the pieces.

If you are able to prove the number of possible solutions or the possible dimensions of the solution, please post your answer! I'm sure the brilliant community would love to see your solution. If you do somehow solve the puzzle itself, take something for that headache you must have and get yourself something nice. This is one of the hardest puzzles I have ever come across, and I know a lot of puzzles. But, let other minds share the same pain that yours did, so please don't post the solution to the puzzle itself. You should still let us know you did solve it, for congratulations, and possibly you can give advice to others who are struggling.

Note by Christian Lee
7 years, 1 month ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

all question in combination in multinomial theorem

- 7 years ago