Shipper's Dilemma

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The Shipper's Dilemma (or Conway's Packing Box) by mathematician John Horton Conway is no ordinary Assembly Puzzle. The version I have, manufactured by Puzzle Crafthouse is a puzzle solver dream, but it can also turn into a nightmare in just a few hours of failed attempts.

There are 17 pieces and they can be grouped into three categories. Counting the smaller five cubes as a unit area, the other two types are 2x2x3 and 1x2x4 cuboids with six pieces each. Your task is to unpack the pieces and be able to assemble them again into a 5x5x5 cube.

The mathematical relations between the three types of pieces is fascinating. For instance, two 3x2x2 side-by-side pieces standing up, have the same length as a 1x2x4 piece lying down... And there are several more lengths relationships between the pieces. You will notice them as you try to solve and analyze the puzzle yourself.

I have seen this concept before, where you have to assemble a certain number of regular-shaped pieces into a given shape. I have two small puzzles in my collection that fall into this category, but with less pieces (both with 9), thus much easier. See here and here. Since I've solve these two in a relatively short time, I thought that the Shipper's Dilemma, while having more pieces, shouldn't be that hard. How wrong I was...

Usually, I like to solve a puzzle before writing a review for it. Not just as a personal goal, but also to have more insight and understanding of the mechanics involved, behind the puzzle itself. This time, however, that requirement wasn't met and I'm yet to solve it. I have been trying unsuccessfully for more than a week and I've lost count how many different ways the pieces were packed.

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An interesting observation by the inventor himself is that the puzzle is almost impossible to solve by randomly assembling the pieces, and I have to agree. The number of pieces involved, which is uncommon for most Assembly Puzzles, makes a random approach pointless, because the possibilities are almost endless. You do have to carefully analyze the puzzle and try to do it in steps, always keeping in mind the very important length relationships between the pieces.

I'm not sure how many solutions are there for this puzzle, but I'm assuming by the nature of the pieces and by the large number of packing combinations, that there are several possible solutions. Finding one might prove to be a tough test to your patience and solving skills. If you know the exact number of solutions, let me know by leaving a message in the post's comments.

EDIT: Thanks to the quick answer by Coaster1235 and contrary to what I previously thought, I know now that the Shipper's Dilemma has indeed 1 unique solution. Proof that this is one devilishly hard puzzle... Feeling challenged enough now?

EDIT 2: Dave Janelle from Puzzle Crafthouse has sent me a presentation with analysis and instructions of the Shipper's Dilemma written by Mike Czerwinski. I gotta say, the analysis is brilliant and it just makes the whole concept seem so simple, that it's used by educators to explain various mathematical principles, such as areas and volumes or size relationships between different cubic shapes. If you're interested in knowing more about this, please contact Dave at Puzzle Crafthouse.

Closing Comments:

Even though I haven't solved it yet, doesn't mean I dislike the puzzle any less. On the contrary. The Shipper's Dilemma is one of the hardest Assembly Puzzles I've tried and I will continue to try it. You are provided with a solution sheet, but I will resist to look at it for as long as I can... Until I give up someday...

Besides the solving part, the presentation of the puzzle is very nice and the quality is flawless. I love the straight lines that criss-cross the entire outer box, which gives it a more elegant look. Oddly enough, I also love this smokey smell of the pieces, particularly coming from inside the cover. Not very commonly "seen" in puzzles, but I still like it.

The Shipper's Dilemma can be found at Puzzle Crafthouse and you can choose between two size models. $13.5 USD for the 0.7lbs version or $16.95 USD for the 1lbs version.

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