HolopTIC

HolopTIC is a 5x5x5 Turning Interlocking Cube (TIC) puzzle designed by Andrew Crowell.  As with HoleyTIC and HolisTIC (Getting Everything Back Together – HolisTIC, HolopTIC has a hole in the middle of each side of the puzzle that runs through the cube.

This one was a lot of fun with some higher order rotational moves.  However, you need to make sure that you don’t cheat on the rotations.  It is possible to make some questionable rotational moves that bypass a sequence of other moves if you’re not careful.

As usual, the more pieces you put together, the more effort is required to add the next piece.  Until you end up scratching your head with one last piece to go.  One piece in particular required a lot of attention.  It didn’t play too nicely with the others and seemed like it would be better to add sooner than later.  Figuring out when and how to add it was the major challenge.

Fairly early on, I singled out a piece that could possibly be added last with a quick rotation but decided that the rotation would be blocked.  However, preliminary tests indicated that the rotation would work just fine.  When I had all the other pieces in place and just needed to add that last piece I verified that the tests were indeed preliminary and not conclusive.  Of course, the piece didn’t just rotate in and was indeed blocked.  Yay!  More puzzling to be had.  Not much longer after that, I had it solved.

I always enjoy solving these TICs and look forward to more to come in the future.  I’m almost at the end of my 5x5x5 TIC backlog.

3-Pronged Puzzling Approach – TritanIC Series (1-6)

A short while ago, just over 5 years, I reviewed a set of 3-piece 4x4x4 Turning Interlocking Cubes (TICs) designed by Andrew Crowell (Puzzle Candy - ThreeTIC, TriadTIC, TripleTIC, NeuroTIC, TriumviraTIC).  These TICs provided quick enjoyable solves to brighten the day.  Recently, a kind soul on the Mechanical Puzzle Discord (MPD) passed on another set of Andrew’s 3-piece TICs that I was more than happy to accept, but this time a 5x5x5 format.

The 6 TritanIC puzzles were designed by Andrew Crowell and like the prior 3-piece TICs, they provide a quick shot of TIC adrenaline to help get through the day.  I managed to hold myself back and do 1 a day over 6 days instead of binging them all in one sitting.
  

TritanIC

TritanIC, which I assume is the first of the series since it lacks a posterior numerical designator, is a nice start to ease you into the series.  One piece has more volume than the other 2 proclaiming itself as the base for adding the other 2 pieces.  The solution requires 1 straight forward rotation.  At least one other nice rotation is possible but not required and it made me wonder if it would be possible to alter the design to require it. 

TritanIC 2

I found TritanIC 2 to be twice as hard and then some as TritanIC.  I took this as a good sign that we were on a good trajectory.  TritanIC 2 has everything you would want in a 3-piece TIC where pieces have to added in orientations far from where they need to end up.  Determining how to simply put the 2 largest pieces together is not a gimme and takes some thought.  And trying to add the smallest piece to the mix is a challenge.

TritanIC 3

TritanIC 3 is a nice follow-up to TritanIC 2.  There are some nice rotations that have to be navigated to get the pieces in place before they collapse into a cube.  And you are almost guaranteed to have to back up and rethink the ordering of the pieces.

TritanIC 4

This is where the trajectory falls apart.  I found this one to be extremely easier.  Less than 2 minutes easy.  If you acquire the series, you may want to start with this one.  The most difficult part is getting the first 2 pieces together, which isn’t that difficult.  The third piece just flops in place before it it closed.  This one didn’t stand up compared to the others in the series.

TritanIC 5

TritanIC 5 gets things back on track.  In fact, it reminded me a lot of TritanIC 3 in terms of approach, rotations, and how the pieces go together.  It’s certainly it’s own puzzle, but has the same overall feel as TritanIC 3.

TritanIC 6

I found TritanIC 6 to be a tricky bugger.  Multiple rotations are required to get the pieces into position before they can start moving into place.  In fact, a few days later, it was non-trivial to determine how the pieces came apart.  A nice way to end the series!

Getting Everything Back Together – HolisTIC

After the last 2 Andrew Crowell spirit-crushing Turning Interlocking Cubes (TICs) that I worked on, 6 Face (Little Nightmares – Six Face) and Templars Cross (A Spirited Journey – Templars Cross),  it’s nice to take a step back and do a little HolisTIC puzzling.

HolisTIC is a 5x5x5 TIC designed by TIC master Andrew Crowell.  It consists of 7 unique pieces entwined in TIC magic.  It’s amazing how Andrew can just crank out all these complex puzzles with his TIC-it-tron.  As it’s name might suggest, there is a square hole bored through the center of each axis making it appear like a well-known Stewart Coffin design.  But this ain’t no Wookey Hole.

Unlike the last 2 TICs I worked on, this one falls on the lighter side TICdom.  I found it very approachable and the solving process moved along smoothly without any major hangups.  Of course, there are the obligatory backup and insert pieces in a different order, but for the most part, the piece locations are easy to determine as well as the movements and rotations needed to get them there.  It’s obvious where each piece enters until you discover that it enters from the other side.  You may also find that the last piece that you need to insert has to be added first.  And then when you do that, you realize that it’s in the way of other pieces forcing you to continually update the order of adding pieces.

Along the way, there are several very nice rotations that play out during the solution to add to the fun.  Some don’t become obvious until the end when you have to rotate pieces out of the way.  I’ve assembled it several times to enjoy the movements along the solution path.  

HolisTIC is obviously a puzzle designed to make you feel better.  And I appreciated restoring some of that confidence lost on 6 Face and Templars Cross.

Andrew’s puzzles can be found on his online shop, ARC Puzzles.

A Spirited Journey – Templars Cross

Templars Cross is as easy as Six Face (Little Nightmares – Six Face), the last Andrew Crowell Turning Interlocking Cube (TIC) that I did.  In other words, I found it difficult.  Six Face had a piece that just gave me problems.  Templars Cross gave me twins to deal with.  Beware the terrible twos(ome).  But let’s start at the beginning.

Templars Cross is a 5x5x5 TIC designed by Andrew Crowell.  The red outer shell encases a 3x3x3 white apparent cube.  Each side of the outer shell has 8 missing voxels basically giving you 6 red crosses on a white background.  Of the 6 pieces that comprise Templars Cross, 2 are mostly red and 4 are mostly white.

Creating the red outer shell is not difficult but adding the white pieces becomes progressively harder.  The first piece is a gimme with a gotcha.  However, the gotcha will be short-lived if you stumble across it.  That leaves 3 little pieces to go.  2 are all white and 1 has a single red cube.  And that single red cube will be your friend once you solve it.

You need to determine how to place the 3 white pieces to make a cube with the white pieces already in the frame.  And do it such that the single empty voxel is cached behind the red frame making the cube appear solid.  And do it so that the frame pieces can be put together.  Did I mention that those twins have to be rotated several times while all this is going on?

The twins are mirror images of each other and are the A and B Soma pieces.  One end of the A piece is red so that has to plug the missing spot in the frame.  Easy, right?  Not so much.  And with all those rotations going on, it gives you an extra opportunity to get the wrong end of the A piece sticking out.

It’s an effort to determine how the white pieces need to be oriented in the cube.  It’s a bigger effort to determine how the pieces need be oriented to get the cube apart.  It’s an even bigger effort to determine how to perform the rotations to go between the 2 orientations.  This is the part that I really struggled on.

After a couple of sessions with Templars Cross, I was beginning to understand the symbolic tie to martyrdom and sacrifice.  I finally decided to throw a Hail Mary and put the pieces in what I assumed was the starting configuration and closed it up.  The only thing to do now was to rotate the pieces until it was solved, taken back apart, or stuck.

Once the frame is closed and locked (yes, one of the pieces acts as a lock), the 2 halves of the frame only shift 1 voxel in either of 2 directions but not both.  It turns out that both are needed in the solution.  I was happy to discover that I had indeed correctly figured out the starting configuration and was able to perform the required rotations to achieve the solved state.  And I find it highly repeatable knowing how Rudolph needs to be oriented.

Little Nightmares – Six Face

It seems that I’ve been on a Turning Interlocking Cube (TIC) hiatus.  Not sure how that happened, but I’m glad to have recently acquired some new Andrew Crowell gems in the 5x5x5 format.  The first one that I decided to tackle was Six Face.  Not Six Faces, Sixth Face, or Six’s Face but Six Face.  I could only assume that it would be a significant challenge and reveal itself as a little nightmare.  Needless to say, it took me longer than expected to solve.

Six Face was designed by Andrew Crowell and my version is 3D printed.  The puzzle is not a complete 5x5x5 cube but looks like a 3x3x3 cube with each face extended outward.  One of these faces is debossed with the name of the puzzle.  The face was carefully chosen so that the name was on a single piece to avoid providing any additional placement clues.  In total, there are 6 pieces that have to be assembled into the final shape.  It only takes 28 moves and there are a couple of rotations along the way.

I took Six Face and several other puzzles with me on vacation to PA, which is ironic since they were sent from PA by kind gentleman looking to spread the frustration.  And by frustration, I mean joy of course.  As always, I overestimated the number of puzzles that I would need.  I started with Six Face and almost ended there as well.  At least I was able to bring it home solved.  YES it was me that solved it!  I’m disappointed that you would even think otherwise.

Solving Six Face took me several sessions.  Right out of the bag, you need to spend 1 of your rotations to get the first 2 pieces together.  Or are they not the first 2 pieces?  Only time will tell.

With the 3 biggest pieces, you can construct most of the visible shape leaving you with the 3 smaller pieces that need to fill the gaps.  Of course, the order of entering those pieces and movements required are what make the puzzle challenging.  Two of the smaller pieces are dancing partners and work nicely to build out the solution path.  But it’s that last piece that is the crux of the solve.  For whatever reason, I had a huge blind spot concerning the where, when, and how of this piece.  It could obviously exist in 2 different orientations, so there were twice as many avenues to explore.  Adding it earlier would provide more room for it to navigate but of course would reduce the mobility of the other pieces.  And just how could that crux piece be added and manipulated into position.

I’m sure it will come as no surprise that a lot of steps were repeated looking for a new avenue to present itself.  With all this experimentation, it became apparent that the final orientation of the crux piece would be different from the orientation that it would enter the framework with regardless of which of the 2 possible orientations was the correct one.  You would think that knowing this, it would be easy to find an orientation where it could be inserted within the frame.  However, I found this a difficult challenge.

Eventually, I found a way to add the crux piece and rotate it into place.  So simple!  How could I have missed it?  All that was left was to determine how to add the dancing partners with it.  Not easy.  Nope.  Not happening.  And it didn’t happen, leaving me to wonder if it was just difficult or if I was barking up the wrong orientation.  At this point I had to split my time between working this approach as well as trying to find an approach for the other crux piece orientation.

Eventually 2, I found a way to add the crux piece in the other orientation and rotate it into place.  So simple!  How could I have missed it?  All that was left was to determine how to add the dancing partners with it.  At least this time, I was able to get everything in place and finally solve Six Face.

Fast forward several months to now when I want to blog about it and take it apart.  No surprises.  The crux piece volunteers to rotate and comes out nicely as expected.  Mission completed!  Except I can’t get it back together!  Try as I might, I just can’t find the exact insertion trajectory.  Unbelievable!  (You’d think by now that I would find this believable).  I spent at least another hour if not 2 getting it back together.  Not only that, I had to check both crux piece orientations since I didn’t pay attention to which one it was when taking it apart.  I’m assuming/hoping that if I take it apart again several months from now, it will be smooth sailing but at this point, I wouldn’t be at all surprised if it were a rough ride.

If you're interested in acquiring any of Andrew's puzzles, you can visit his online store ARC Puzzles.

Puzzle Complexity

In the last blog, I mentioned that The Nagging Wife puzzle had a level of 3.1.2 difficulty without really explaining what it means.  If you see a string of numbers like this separated by periods, it is usually the number of moves required to remove the pieces from the puzzle.  In the case of The Nagging Wife, it takes 3 moves to remove the first piece, 1 to remove the second, and 2 to remove the third.  For many puzzles, this is used as a proxy for its difficulty.  As the number of moves increases, the puzzle is generally more complex and difficult to solve.

In reality, puzzle difficulty is completely subjective and although there may be a general consensus on the general difficulty of a puzzle, everyone is different and has their own perspective.  For instance, Hanayama puzzles come with a rating of 1 to 6 stars with 6 being the most difficult.  I particularly like the old style boxes with the die showing the level of complexity.  When a new puzzle is released, there are sometimes frequent mutterings on the miscasting of the difficulty within the puzzle community with some saying it was too low and others too high.  As I get older, it seems that the number of stars is skewing too low.

In 2017, I gave a speech on puzzle complexity and provided the following clues for gauging the difficulty of a puzzle:

Suggested Level – If the puzzle is mass marketed, it probably comes with a suggested level of difficulty.  In some cases, the level may be provided by the designer.  After all, these designers are the world's greatest puzzle experts and have a lot of experience with puzzles and how well people can solve them.  If you’re new to the puzzling world, you may find them underestimated.  If you are an experienced puzzler, you may find them overestimated.  Look for the ones with the icon of the guy pulling his hair out for the best puzzle experience.  I know quite a few bald puzzlers.

5 Piece Plate Burr
Delight by Stéphane Chomine

Number of Pieces – Piece count can be an indication of difficulty.  The more pieces that there are to work with the more difficult it usually is.  Of course, a 5 or 6 piece plate burr puzzle could easily be more difficult than a 2000 piece jigsaw puzzle.

Piece Variety – Usually puzzles where all the pieces are different are more difficult than when they are all the same.  When they are all the same, you don’t have to worry about where each piece needs to go relative to the others.  This could be a factor of N! for mathematicians.

Moves Required – In general, as the number of moves required to solve the puzzle increases, the complexity of the puzzle  increases.  However, some puzzles like N-ary puzzles may require very large numbers of moves to solve but may not necessarily be difficult.

N-ary Puzzle - Spin Out by William Keister

Piece Shapes – Everyone is really comfortable solving a cube dissected into smaller cubes.  Smash it, stretch it, skew it, and deform it in so many unspeakable ways and it becomes intimidating.  Haym Hirsh has been doing a nice job recently of distorting 3x3x3 cubes (Inelegant Cube, Inelegant Box, Somaa, Jitter Soma) by using pieces that aren’t cubic and some that leave gaps in the solved state.  It messes with your head when the pieces are no longer flush against each other when building the cube and once you start cutting pieces at non-right angles, things get much more complicated for the designers, craftsman, and puzzlers.

Burr vs. Disentanglement
Wookey Hole by Stewart Coffin
and Man-O-War

Puzzle Type – Most puzzlers have a preference for the types of puzzles that they are interested in at the moment.  Give a hard-core burr puzzler a rookie disentanglement puzzle and he may struggle like a newbie.  That’s what makes it so fun!

Rotations – For cubic dissections, the trend has been moving towards creating Turning Interlocking Cubes (TICs).  I believe that Bernhard Schweitzer coined this phrase while doing a study on TICs.  When solving a burr, knowing that a rotation is required is a significant clue.  It activates all sorts of additional puzzle solving neurons in the brain while working on a puzzle.  When you are completely stuck on solving a burr, you eventually ask whether a rotation is required.  If the answer is yes, you happily go on searching for the rotation.  If the answer is no, despair settles in.  It’s as simple as that.  Andrew Crowell is the current master of creating cubic dissection puzzles with rotations and they are all recommended.

Coordinate Motion
NOS 5 Crenel by Gregory Benedetti

Coordinate Motion – Movements with pieces simultaneously going in different directions can add to a puzzles complexity.  In many cases, getting all the pieces that have to move at the same time in position can be a real dexterity challenge like Rosebud by Stewart Coffin.  One of my favorite coordinate motion puzzle designers is Gregory Benedetti who did a spectacular job with the New Old School (NOS) Burrs.

Number of Solutions – Many packing puzzles have multiple solutions.  In general, it is expected that as the number of solutions increases, the chances of finding one becomes easier.  For instance, the Soma Cube by Piet Hein has 240 ways to create a 3x3x3 cube and it is not that difficult to find one.  The Half Hour puzzle by Stewart Coffin, however, has only one way to create a 3x3x3 cube and is much more difficult.  I’m guessing that the Half Hour puzzle was named for how long it took Stewart to make the first copy of the puzzle given how much longer it took me to solve it.

Two 3x3x3 Cubes - They Don't Look That Different!
Soma by Piet Hein (Left) & Half Hour by Stewart Coffin (Right)

Cord Length – For disentanglement puzzles, the length of the cord is usually just long enough to accomplish the solution.  The longer it is, the higher probability that you can tie it into a knot.  Beware if it is long enough to hang yourself with.

I’m much more careful now about giving out information on puzzle difficulty after an extremely embarrassing faux pas.  While attending my first International Puzzle Party, hobnobbing with the cognoscenti of puzzledom, I put some of my puzzles out in the hotel lobby for others to play with.  One attendee asked me if one of the puzzles was difficult to solve.  It's easy I told him and then watched him struggle for hours trying to solve that puzzle.  I think that he may have been shamed by my comment into trying to find the solution and instead of enjoying the puzzle, it may have become a burdensome task.  Of course, I like to think that, like myself, he enjoys being frustrated.  Why else would we do it!

If you are interested in the Man-O-War puzzle, you can find it at PuzzleMaster along with Hanayama Puzzles, the Soma Cube, and the Half Hour puzzle.