Is Metagrobological Science Broken? - EnigmaTIC

Breaking News - Is Metagrobological Science Broken?  Recent events have questioned the very foundation of the Metragrobology community, leaving many puzzled.  An EnigmaTIC challenge is perplexing the experts.  Assessing the complexity of this conundrum is the conundrum.

Way back, a long, long, time ago, when I was a wee tad, my granddaddy put me on his knee and said “Son” (I don’t know why, but for some reason granddaddies always say son to their grandsons.  I guess it’s one of those economy of expression things even though my granddaddy wasn’t a C programmer).  “Son”, he said, “There are many important things in life you need to know and some are more important than others.  However, the one thing that you mustn’t forget is that if a quantity of cubes forming a completely filled PxQxR rectangular parallelepiped is divided into sets comprised of cubes that form a single contiguous entity, there is a way to divide the sets into 2 non-empty groups such that one group can be separated from the other along a single Cartesian coordinate system vector, if and only if it is possible to separate the pieces from each other”.  I always knew that no matter what else was happening in the world, I would always be comforted by this knowledge.

Now imagine my shock, when a good friend and highly respected metagrobologist declared that “I've found a space filling (all 64 voxels) design that requires more than one move to free the first piece. In fact, it requires several moves.”  Wow! That just shatters the metagrobological foundation that underlies all my puzzle knowledge.  I've come up with ways to do it with non-cubic dissections but not a straight-forward 4x4x4 cubic dissection.

So how did this whole kerfuffle get started?  On several of my Turning Interlocking Cube (TIC) posts, I explained that if there were no voids within the puzzle, the first piece can be pulled out in one move.  Andrew Crowell, the TIC master, thought that this sounded a bit fishy and set out to demonstrate that a cubic dissection puzzle with no voids could be developed requiring multiple moves to free the first piece.

I was saying to myself, “No Way!”, even though this announcement was debuted as a comment on my post where I declared, in a rather PedanTIC manner, that I had learned my lesson and that the correct way to approach a puzzle is with an open mind (see The Correct Way to Solve a Puzzle - PedanTIC).  How could it possibly be done?  I finally decided that it had to use the 4th dimension.  I always have problems envisioning how things look with that 1 additional dimension.

When the pieces were released, I immediately created a set and solved it very quickly.  There are 6 pieces and I used maple to make them.  The puzzle is not difficult to assemble, but the required rotations make it interesting.  When I solved it, it reminded me of Stuart Coffin’s classic, Wookey Hole, although that puzzle is a 5x5x5 cube and has conspicuous voids in the final assembly.

In honor of the ensuing controversy, Andrew named the puzzle EnigmaTIC.  So where did things fall apart and what did Andrew create?  In a prior post, I explained how the complexity of a puzzle is sometimes defined by how many moves it takes to remove the pieces (Puzzle Complexity).  Both BurrTools and Puzzle Will Be Played (PWBP) provide this information for a solution. 

The problem was incubated in my lazy description of both puzzle complexity and how it relates to puzzles without voids.  I’m sure that I would be severely reprimanded by my granddaddy if he were still around to set me straight.  I still hide the rulers in the house.  What I should have said was that the complexity was a description of how many moves it takes to remove something from the puzzle, where that something could be a piece or a subset of pieces.  This is the convention used by both BurrTools and PWBP.  There are many instances of puzzles where more than 1 interlocking piece comes out in 1 move like Wookey Hole.  In fact, my very first interlocking puzzle, the Kimiki Cube (In The Beginning – The Kimiki Cube) has 2 pieces that come out together in one move.

My apologies for the carelessness that started this kerfuffle, but we did get a new cool TIC puzzle out of it, so I don’t feel so bad.  Have I mentioned that I didn’t think it is possible to create a really cool 5x5x5 cubic dissection with a minimum 10 pieces that takes at least 25 moves to remove the first piece, or set of pieces, and each piece requires a rotational move to extract.

Earth Day Celebrates 50 Years - Globe Ball

Thousands of casualties in the animal world resulted from the 1969 oil spill off the coast of Santa Barbara.  Earth day was established the following year on April 22nd to raise awareness for environmental reform.  Today marks the 50th anniversary of Earth day, which is now celebrated around the world.

In honor of the 50th anniversary, I searched for a puzzle that would have a global appeal.  The obvious choice was Hanayama’s Globe Ball puzzle.  Unlike most Hanayama puzzles, this one is plastic and twice the normal size.  However, similar to several of the Hanayama puzzles, this one was designed by Vesa Timonen. 

Vesa’s original design was called Tangerine and entered in the 2008 Nob Yoshigahara Puzzle Design Competition, where it won a First Prize award.  Like a tangerine, the internal pieces consisted of wedges that make a complete sphere and there are 4 of them.  The peel of the tangerine wraps around the wedges and is divided into 2 pieces, reminiscent of the outer skin of a baseball.  The skin covers all the segments except for a small hole where you can use the tips of your fingers to rotate the segments within the tangerine.  Once the segments are in the proper position, the tangerine can be opened to free the segments.  However, this is not as easy as it sounds since you can’t see through the peel to see if the pieces are in the correct position.  All you can see are the edges of the segments as they rotate past the access hole.  This requires you to look at the edges and then rotate them while mentally trying to track where they are after they leave the opening.  Of course, all this assumes that you have determined how the segments need to be oriented to open the tangerine.

The original version of Tangerine was 3D printed using orange for the peel pieces and white for the segments.  For the Hanayama version, an additional layer was added to the puzzle and renamed Globe Ball using the Earth as the new theme.  The molten core has 4 red segments surrounded by 2 blue oceanic pieces.  The 2 new outer shell pieces are a transparent light blue with opaque white regions depicting the continents.  Now instead of having a single outer shell, there are 2, and the inner shell needs to be manipulated into position with respect to the outer shell.  This has to be accomplished while still manipulating the internal core segments through the hole that is now in both shells.  Another nice feature is the addition of a 3rd outer shell piece that screws into the hole making the globe a complete sphere.

The packaging for Globe Ball deserves some recognition.  The box is a simple transparent box showcasing the puzzle and all the inserts.  Everything is very neatly packaged and the Ball is cradled between 2 clear plastic inserts.  The plastic insert on the bottom covers the official base to display the puzzle.  Another nice feature is that the box not only provides the puzzle designer’s name but has his photo as well.

After solving Globe Ball or the original Tangerine, you can see where the inspiration for Vesa’s newer puzzle, Cast UFO (Uns@lv*bl# F!&#ing O$j@ct - Cast UFO), came from.  You can almost hear him say, I want to do something similar but totally different.  And he did.

Globe Ball is difficult to come by and I’m glad I was able to acquire a copy.  It is not a very difficult puzzle but it is very clever and displays well.

The Proper Way to Solve a Puzzle - PedanTIC

There is a right way and a wrong way to solving a puzzle.  The right way requires that you have an open mind with the ability to explore all possible solution paths.  Of course, puzzle designers know that you’ll go the wrong way and they'll do everything in their power to make that the most attractive path to the point where you can no longer see the correct path.  This was the lesson that I learned during last month’s Andrew Crowell Rotations and Obstructions Series - Turning Interlocking Cubes (ACROSTIC) series challenge: BioTIC (Green Beer ‘ill Cure What Ails Ya - BioTIC).

I applied what I learned solving BioTIC to this month’s ACROSTIC challenge: PedanTIC.  It also turns out that PedanTIC shares a lot of similar characteristics with BioTIC.  Although the pieces and moves are different, they share many of the same qualities and the description for BioTIC can almost be copied for PedanTIC - except that I was not caught unaware this time!

What are the similarities?  Like BioTIC, the first 2 pieces of PedanTIC can be pulled from the assembled puzzle in 1 move.  The third piece, however, takes 2 moves instead of 1.  These 3 pieces are mostly space fillers that allow you to figure out where the remaining pieces go.  All the real fun is in placing the remaining pieces where they need to go.  And what fun it is!

PedanTIC consists of 5 pieces that have to be packed in a frame to form a solid 4x4x4 cube.  As I sat there in quarantine playing with PedanTIC, I started to daydream about those last 2 pieces. The spikey ball piece looks like the SARS-CoV-2 virus and once it’s in the main body of the frame, it moves around without seeming to have a way of being removed.  Another piece acts a receptor for the SARS-CoV-2, which I’ll refer to as ACE2, and as they dance around in the cage, the SARS-CoV-2 virus attaches itself to the ACE2 multiple times.  Of course, once PedanTIC is completely assembled, the SARS-CoV-2 virus is in contact with all the other pieces including the frame.  Yes, we all seem to be a bit preoccupied with the latest Coronavirus - Wash your hands!

After my experience with BioTIC, I was able to solve PedanTIC in fairly short order.  My advice to anyone doing these 2 puzzles it not to do them back-to-back (albeit a month apart) like I did.  Throw a PackTIC or 2 in between.

This is the fourth post of the monthly ACROSTIC series.  You can find the prior posts of the series here:

• January: Puzzling DNA - GeneTIC
• February: TIC, TIC, TIC - PackTIC II
• March: Green Beer ‘ill Cure What Ails Ya - BioTIC

Here Comes Peter Cottontail - Kimiki Bunny

I found the perfect puzzle to highlight the upcoming Easter weekend.  This was going to be the coolest puzzle post ever.  One heart-stopping description after another documenting the brilliant execution of the solution process culminating in a series of vivid photos capturing the essence of the final state of puzzle completeness and tranquility.  I was pre-basking in the glory of the deluge of comments that would be coming forth from puzzlers around the world astounded by my puzzle solving prowess.

Too bad I was unable to solve it.  Tranquility was out the window not to mention how far away from the final state of completeness I was.  With a dozen pieces continually mocking me, I realized that I would not be able to solve that puzzle in time for this post.  Maybe it will get done for next Easter or some other Easter in a year starting with 2.

It was at this point that I needed a significant confidence booster and pulled out my good buddy Peter Rabbit.  Peter spends most of his time in a cabinet as part of my original puzzle collection from the 70’s with several of his other Kimiki buddies.  Not only is Peter good looking but he’s musically inclined as well, being equipped with a bell that merrily jingles as he hops along.

Altogether, Peter is comprised of 10 pieces.  To assist in the assembly, there are multiple anatomical hints to help you get your bearings.  The astute puzzle will be able to leverage these hints.  For instance, the face is drawn across multiple pieces and you can use that to orient them when constructing Peter.  The puzzle is cleverly designed to split the 2 eye circles in half across pieces.  This is reminiscent of Jos Bergmans’ Sun puzzle where you have to mate the 2 halves of a circle but Kimiki Bunny takes it one step further and has 2 split circles that have to be reunited instead of one.  Some puzzlers may find this tricky and if you aren’t careful, you may end up with something like cyclops zombie bunny.

It’s always nice to successfully solve a 10-piece puzzle.  If you find that this puzzle has too many pieces for you to handle you could try something with fewer pieces like Mega Six by Bill Cutler, which has roughly half the number of pieces as Kimiki Bunny.

The First of April - Fool’s Cube

It’s the first of April, and we all know what that means.  It’s a time for tricks, pranks, and of course, PUZZLES!  Since this post falls exactly on that magnificent day, I decided to celebrate by creating a little puzzle.  The design criterion was simple.  No, coming up with the design criterion wasn’t simple, the criterion itself was to be simple.  I don’t know why it’s so complicated to describe a simple criterion.

Simple in this context was a 3x3x3 cubic dissection that would be within the capabilities of most wood tinkerers to make.  That provided 27 cubes to work with.  To make it even easier, I decided that it had to be interlocking.  Anyone familiar with 3x3x3 puzzles knows that you really can’t make a difficult interlocking puzzle in that format, even if you wanted to.  Although, I was tempted to add half-cubes and add rotations, I stuck with the design criterion and kept it simple.  However, it still has a nice Aha moment to be enjoyed.

In honor of this fabulous holiday, the puzzle was named Fool’s Cube.  Since I haven’t started working in the garage shop yet, I made the prototype from some Cherry and White Oak pieces left over from past projects.  I was 3 cubes short of being able to make it all in Cherry.  Since there are only 4 wooden pieces, I decided to drill a hole in each and put them on a keychain.  This way, I can easily carry the pieces together and hand them to someone to solve.  I didn’t have an appropriate keychain and the one that I made is too large.  I’ll need to shop around for a more suitable one and plan on getting one of those nylon coated stainless steel wire keychains.

Fools’ Cube has a difficulty of 1.2.1 and there are no rotations.  You could put it in BurrTools and it will not only provide the assembly but show you step-by-step how to put it together, but don’t waste your time doing that.  Just build one and solve it on your own.  It will take you a lot less time solving it than building it.  If you do make one to try, you should time yourself to determine how long it takes you to put it together.  Most of you will do it in a couple of minutes.  Let me know how you do.  It took my wife a minute and a half.