Calibron 12

Posted on Jun 6, 2012 by Gabriel | 10 comments
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(Click to Enlarge)
Today's puzzle is a classic dating back from 1933. The Calibron 12 is a fascinating packing puzzle invented by Theodore Edison, son of Thomas Edison. The original copy can be seen in Jerry Slocum's collection.

Suggested by its name, the puzzle is a selection of 12 rectangular blocks with different sizes that need to be placed inside the provided frame. There are two identical pairs of pieces, though. Sounds easy enough, but it's actually one of the hardest packing puzzles I've tried so far.

The Calibron 12 is beautifully presented in this 18 x 23cm (7" x 9") stylish frame with an extra space for a piece so that it comes unsolved. The pieces are a mixture of four different types of precision cut woods, resulting in a unique combination of colors from a wide selection used at Puzzle Crafthouse's shop. Each piece has its own relative size engraved, so it's very easy to identify them and see the size relationships between them. It can also prove quite helpful in a mathematical analysis.

The packing area measures 16 x 16cm (6.3" x 6.3"), which corresponds exactly to a square measuring 56 x 56 units. It's also known that the total area of the pieces is 3136 units. Knowing the relative size of each piece you have all that it's needed to solve this problem mathematically... If you can.

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I got this puzzle a few weeks ago and up until the time of writing, I'm yet to find a solution. In fact, there is only one possible arrangement for the blocks that can fit the 56 x 56 frame. There are other theoretically possible rectangle areas, like 112 x 28, 64 x 49 and 32 x 98, however they can't be solved with these particular pieces. This may be a challenge for you to see which piece sizes would be needed in each rectangular area. With fewer pieces you can make many smaller rectangles and attest that the blocks have all kinds of possible combinations and arrangements. Finding the correct one, well, that's a whole different mater.

The puzzle is rated as a 5/5 level of difficulty, and I couldn't agree more. Although perfectly possible, I believe it's extremely difficult and unlikely to find the solution just by randomly packing the pieces. Unfortunately, I'm not a math wiz, so tackling the problem by mathematical analysis is out of the question. I read an interesting article explaining the methods for packing different rectangles in a frame, but for a layman it's not easy to wrap your brain around it. I will continue and try to find the solution the old fashion way. I reckon if I'm persistent, I'll eventually find it... Or not.

Closing Comments:

Even though I'm yet to find the solution for the Calibron 12, I love it! It's a simple, but brilliant concept, and the way that it's presented makes you want to try it, even if you don't dominate the math field. If you're a math geek, this is the perfect puzzle for you to put your skills to the test.

Availability: This particular version of the Calibron 12 can only be found at Puzzle Crafthouse and it's available for $27 USD.


George said...

I also found this puzzle too difficult to solve by hand. I solved it using BurrTools. The next paragraph gives a small hint, stop reading now if you don't want one ...

There are two pairs of identical rectangles. In the solution, the two 21x18 rectangles do not touch one another, but the two 21x14 rectangles share an edge and can be combined into a rectangle of twice the area.

Gabriel said...

Thanks for the hint, George ;-)
I'm sure it'll still be a pain to solve, despite the help.

George said...

By the way, the puzzle is not easy even for BurrTools. On my PC, it takes BurrTools 40 minutes to show that there is only one solution.

Gabriel said...

Wow, that is impressive. And an interesting fact about the puzzle is that when it was originally designed, the description was that the pieces formed a rectangular area, but this area was not specified. Pavel Curtis sells this puzzle too, but without a frame, which is even harder a challenge.

George said...

Yes, I have Pavel's version. Indeed, he doesn't even tell you the dimensions of the tray! Curiously, many of the piece dimensions are multiples of 7, but I wasn't able to figure out how to exploit this. But perhaps there is a clue there.

Gabriel said...

Indeed, you're right. I didn't notice this at all. Now that you mention it, even the dimensions of the frame are a multiple of 7 - 56 x 56. Very interesting...

Cookie Monster said...


I wrote a small routine in Excel that solves this puzzle (and any other that is 2D with rectangles) : https://docs.google.com/file/d/0B5EceiQ4zjqRU0lFTzhBU3ZXSVU/edit?usp=sharing

The routine basically tries any possibility and finds the Calibron12 solution after 400k tries, which takes about 30 seconds (or a bit more with the grid animation turned on).

Have fun :-)

Unknown said...

I finally found a solution by trial and error after 16 hrs. over a period of 2 weeks. I was surprised at how unsatisfying that was because now its over.

Gabriel said...

Wow, I admire your patience. I was never able to solve it on my own. But hey, that one might be over, but there's lots of other great packing puzzles out there to enjoy.

Anonymous said...

Solved it!....in less than a year!!.....hint below

set the four pieces with even dimensions aside......till you need them

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