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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
4 years, 2 months ago

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4 votes

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all question in combination in multinomial theorem

Jayant Sarkar - 4 years, 2 months ago

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