# It's a triple cross variation puzzle

I've been trying to solve this puzzle for a long time.

When I got it, it was wrapped in plastic with no description on how to solve or what it's official name is.

The only other description it had with it was limited edition.

Can anyone help me solve this puzzle?

• Could you please describe where it came from? How you got to this puzzle? Who sent it to you? Could you also take a slightly better pic? Sorry :P – NL628 Jan 14 '18 at 2:56
• This looks like a Burr puzzle. – Otami Arimura Jan 14 '18 at 3:27
• I would like to leave FLEB's video on Burr puzzle. It is not the exact same pieces, but it may give you some hints. – Otami Arimura Jan 14 '18 at 3:29
• I checked the inventory of Gemani Games and Brilliant Puzzles, since all my burr puzzles with that particular wood color are from those two online stores. Couldn’t find a match for these exact pieces. – Bass Jan 14 '18 at 8:25
• Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) – Rubio Jan 30 '18 at 9:10

The first thing to notice that this isn’t going to be a “complete” burr, there is no final key piece that you could just slide in to lock the puzzle. This means that there will be empty spaces inside the solved burr, so it’s quite likely that some of the pieces can move a bit without the burr coming apart.

Therefore, not only will you have to figure out the proper alignments and order of the pieces, you’ll have to find a way to wiggle the pieces to their interlocking configuration.

The surefire way to approach these puzzles is the systematical one. Give a name to each piece, develop some kind of notation for the position and orientation of each piece, and start to go through all the possible combinations in some order that goes through all the possibilities eventually.

This seems like quite a big task: there will be quite many possibilities. Most of them will prove impossible very early though, either by blocking another dimension’s pieces, or obviously leaving some of the slots visible in the completed burr.

The above filtering will exclude most of the possibilities even without checking more than the pairs of parallel pieces separately. If you are brave, you can even skip it in the beginning, and start from the next step.

The next step is to try to find a suitable combination of positions and orientations for the pieces. I find the best way is to build the horizontal pairs separately on a table, and the vertical one in hand. Then, only if the arrangement seems plausible, try to figure out how to actually put the pieces together. This is pretty much a trial and error thing for me; the only bit of system is the choice of the final piece to go in.

This should solve even the most difficult interlocking burr puzzles, but it can take quite a bit of time (a couple of hours) if the burr is very complex. Judging from the relatively simple shapes of the pieces in the picture, that one probably isn’t at the very deepest end of the complexity pool. Given that it’s “special edition”, it may even have so few options that it’s actually unsolvable. Proving unsolvability will be impossible without the systematic approach. (No cheating with computers allowed!)

TL;DR: Good luck, and remember to only touch 3 or more pieces together when you already have a solution in mind!

• I disagree with your reasoning about no final key piece automatically meaning there must be holes. It could be that pieces #2 and #6 in the photo combine to form a key that slots in to form a solid finished puzzle. However, it seems you are right in this case. Counting the volume of these pieces shows that there will be a single empty cube inside. My packing program shows that there are 3 ways for these pieces to fit inside the final shape (none with #2 and #6 as a single key) but I can't visualise it well enough to know which of those can actually be assembled by some move sequence – Jaap Scherphuis Jan 14 '18 at 8:57
• @jaapscherphuis, Oh yeah, completely forgot about that possibility. So if you roll piece 2 up by a quarter turn, and place piece 6 across it, slot down, you indeed get a piece that could completely fill the burr. Great catch! – Bass Jan 14 '18 at 9:31
• There are also solid burrs where two sets of 3 pieces slot together. Looking at the three packing solutions of the pieces in the question, I don't see any way they can be put together at all. I'll have to dig out my lovely Pentangle Chinese Cross Compendium and try this one out for real. – Jaap Scherphuis Jan 14 '18 at 9:39

This is a very sneaky burr puzzle, because it involves a bit of a trick:

There is a twisting move. Piece #1 (i.e. the top one in the photo) has a thinner middle section, maybe even rounded slightly, that allows it to be rotated when in position.

Number the pieces in the photo from #1 at the top to #6 at the bottom. In the finished puzzle shape, the pieces occur in pairs of parallel pieces. Those pairs are:

#1 and #5
#2 and #6
#3 and #4

Here is a sequence of photos showing how to assemble it.

Photo 1: Place piece #4 perpendicular to and inside #6
Photo 2: Place #5 perpendicular to both #4 and #6.
Photo 3: Place #1 parallel to #5, but rotated a quarter turn so that it is out of the way.
Photo 4: Place #3 parallel to #4.
Photo 5: Place #2 parallel to #6, in between #1 and #5
Photo 6: Rotate #1 to lock around #2 and #6.

My #1 piece is not thin enough to allow the rotation move, so I can't show you the finished cross shape with these pieces.