Serendippity

Some amazing puzzles have recently come to my attention and I decided to adorn a round table with a nice selection of them.  All of these puzzles competing for my attention.  What serendippity!  For no particular reason, my goal was to spend Wednesday through Sunday solving them.

Canal

Canal was designed by Han Dongkyu and consists of 4 pieces that need to be placed in a tray so that there is a path between the pieces from the lower left-hand corner to the upper right-hand corner.  And the path can only be a single unit wide.  And there can be no other uncovered squares in the tray that are not part of the path.

I’ve been seeing photos of Canal for a while and had always wanted to give it a try.  It seemed like a novel idea and how hard could it be with only 4 pieces that needed to be placed in the tray.  Well looks can be deceiving and it took me a bit of time to find the correct orientation and positioning of those pieces.  It was a very nice challenge and is currently available at Team JB Hobbies.  Canal was also an entry in the Nob Yoshigahara Puzzle Design Competition at the 43rd International Puzzle Party (IPP43)

Bocca Della Verita

Bocca Della Verita is a 2D restricted-opening packing puzzle designed by László Molnár.  It consists of 7 L Tromino pieces that need to be packed in a circular tray.  Each piece has to be entered through the maw in the top.  Two other openings are provided to poke your finger into for manipulating the pieces inside.

I solved this one a while ago but without the fancy restricted-opening top.  With the top, it looks much move daunting with limited opportunities to move pieces around and I was wondering how much more difficult the dexterity aspect would make it.  Although certainly more challenging, it turned out to be quite doable.  And just like Canal, it was an entry in the IPP43 Nob Yoshigahara Puzzle Design Competition.

Diasafe

Diasafe is a restricted, somewhat 2D’ish packing puzzle designed by Lucie Pauwels.  It consists of a variety of 8 pieces made from 3 to 9 squares.  Each piece has a button added on top of one of it’s squares.  And all 8 pieces are unique.  The frame that holds the pieces has a slot in the side to add the pieces and a Z-track on top for the buttons to slid through.  

The objective is to add the pieces to pack the frame by entering them through the slot in the side and moving them where they need to go.  Of course, the movements of the pieces are restricted by the Z-track on the top of the box.  Since all the pieces are different shapes and sizes, enter from the same point, and have to follow the same path, the challenge is to find how they are packed and the order to add them. 

On my initial solving attempt, I added all the pieces to the frame but subsequently found out that all the buttons had to be in the Z-track and not in the single-square entrance to the Z-track.  Backtracking a bit, I found a solution where all the buttons properly resided within the Z-track.  The addition of that final restriction added some nice additional properties to the solve.  And coincidentally, it was also an entry in the IPP43 Nob Yoshigahara Puzzle Design Competition.

Elegant People

Elegant People was designed by George Sicherman and made by Wood Wonders.  It consists of 4 pieces, each constructed from 3 cubes with most cubes attached with an offset.  Each pair of pieces can be used to construct a symmetric shape resulting in 6 challenges.  I’ve been working on this one for several months and have still not completed it.  Of the six challenges, some are easy, some are more challenging, some are difficult, and one is downright impossible.  Apparently, some elegant people are more difficult to get along with than others.  This is a fantastic set of challenges that transports easily.  A must have for symmetry puzzle enthusiasts.  Eventually I’ll figure out that last one.  Stubborn little bugger – THE PUZZLE!  And as incredible as it is to believe, it was also an entry in the IPP43 Nob Yoshigahara Puzzle Design Competition.

Loach Bed

Loach Bed is an apparent cuboid packing puzzle designed by Osanori Yamamoto.  It consists of 3 simple pieces that need to be packed within a 2x2x3 box with a single 1-voxel corner missing.  I solved this one last year at a puzzle picnic and took this opportunity to revisit it.  This is one of Osanori’s simpler packing puzzles but works well in a small format.  It’s a good packing puzzle for someone just being introduced to 3D packing puzzles since it has a simple entry point, few simple pieces, and takes several moves to remove the first piece once solved.  And to top it off, it was an entry in the IPP43 Nob Yoshigahara Puzzle Design Competition.  And furthermore, it won a Top 10 Vote Getter award in the competition.

One Way or Another

One Way or Another, designed by Alaexander Magyarics, presents a nice 2D sliding puzzle challenge.  Not only do you have to solve it, you have to design it as well.  The ultimate objective is to move the small round piece from the upper right-hand corner to lower left-hand corner by finding a sequence of moves that allows the round piece to traverse the tray also holding the other 4 pieces.  However, the first and significantly harder objective is to discover how to pack the pieces in the tray to accomplish the ultimate objective.

Since there are multiple ways to place the pieces in the tray, especially since there are 4 unoccupied spaces, it looks quite daunting.  Maybe I got lucky, but focusing on the location and interaction of a couple of pieces, I zeroed in on a working configuration much quicker than I expected.  Of course, I was expecting the worst.  The final configuration provided a longer sequence of moves to solve the puzzle than I anticipated.  The length of the solve makes identifying the design less obvious.  Even so, the real challenge here is to design the puzzle rather than solve it.  The solve really serves to validate the design.  This was a very nice novel concept which resulted in a Jury Honorable Mention award at the IPP43 Nob Yoshigahara Puzzle Design Competition.

Thyor

Thyor is a 3D restricted-opening puzzle designed by Volker Latussek.  It consists of 6 pieces that need to be packed within a box with a single opening.  But open it is.  The largest side of the box is entirely open except for a single voxel overhang on all sides.  You can just start dropping the pieces in up to a certain point.  

The pieces are made from 3x3x2 cuboids.  There are 3 types of pieces: 1 of the first type, 2 of the second, and 3 of the third.  I found this one quite challenging and was happy to eventually end up with all 6 pieces packed inside the box.  And would you believe, it was also an entry in the IPP43 Nob Yoshigahara Puzzle Design Competition.

Petit Albert

Petit Albert was designed by Volker Latussek and consists of 5 pieces that need to be packed within a 2x3x3 box.  The box has a 3 voxel opening on one the 2x3 sides to add/remove/manipulate pieces.  There are no other openings in the box.  The pieces consist of 4 tetracubes and 1 dicube.  Each of the tetracubes sports a rounded corner that allows an additional rotation within the box.

I originally solved Petit Albert last year (Round Bevels – Petit Albert) but it was definitely worth a revisit.  The second time around, it was still a good challenge and I had to rediscover the Aha moment.  There are quite a few rotations and a bit of dexterity involved.  Just like the first time, I found it a challenge to repeat the sequence of rotations within the box that were found outside the box.  A winner for sure.  I can’t wait to see Fat Albert.  Hey, Hey, Hey!

And believe it or not, this puzzle was also an entry in the IPP43 Nob Yoshigahara Puzzle Design Competition.  Where it didn’t win anything.  Which is a shame because I found it a tough little nut with the rotations that were required.

Round Bevels – Petit Albert

There’s some severe beveling going on with Volker Latussek’s latest 3D packing puzzle.  Why?  Because it introduces the ability of the pieces to perform an additional rotation within the box.  Of course this extreme beveling is not beveling at all but rounding where the edge is rounded with a specified radius instead of a simple angled cut. 

Volker Latussek has been generating a plethora of petit packing puzzles in the 2xXx3 format.  The puzzles use a variety of box shapes, openings, piece shapes, holes, rods, spheres, drawers, trapped pieces, and more.  This is the story of Petit Albert.

Petit Albert consists of 5 pieces that need to be packed within a 2x3x3 box.  The box has a 3 voxel opening on one the 2x3 sides to add/remove/manipulate pieces.  There are no other openings in the box.  The pieces consist of 4 tetracubes and 1 dicube.  I’ll avoid naming the pieces to avoid aggravating any sensitivities that various readers may have due to the lack of a definitive naming convention.  I’ll just say that the 2 types of tetracubes are mirror images of each other and that there are 3 of 1 and 1 of the other.  AND!!! the 3/1 split is aligned with the shape of the box opening.  Don’t change one without the other.

Each of the 4 tetracubes has a rounded corner where the radius of the round is equal to the voxel size.  This allows an additional rotation that would have been blocked by an intact corner.  This extra degree of freedom provides one more tool in the bag for solving the puzzle.  Of course in reality, it’s really one more tool used by Volker to confound your solving process.

I found the hardest part of the solve was convincing myself that I had indeed found how the pieces are assembled within the box.  The assembly has some easy to recognize desirable features and yet still appears to fall short due to the difficulty in seeing how the pieces can be manipulated into their required positions.  I’d almost go as far as to say that the first piece to be added to the box is the most difficult to get in place.  Almost.

Petit Albert provides a good mix of assembly, piece interaction, and rotational movements that make this puzzle a winner.  I believe that it will be available as part of the next Pelikan release and I definitely recommend adding it to your collection if you have been enjoying Volker’s other petit puzzles.

3Y + 1W Conjecture – Collatz

A puzzle being solvable is only conjecture until it can be proved that it is possible.  Some folks use fancy shmancy mathematical proofs while the rest of us just bash our heads against it until it yields.  Or doesn’t, in which case, Q.E.D., it is relegated to the obviously unsolvable pile.

On the mathematically unsolvable pile lies the Collatz Conjecture.  The objective of this puzzle by German mathematician Lothar Collatz is to prove that any positive integer can be reduced to 1 in a finite number of steps where at each step the number is divided by 2 if it is even or multiplied by 3 and added to 1 if it is odd.  Yes, puzzlers aren’t the only community to dedicate time to solving capricious whims and fancies.

Taking inspiration from this unsolved mathematical puzzle, Dr. Volker Latussek transmogrified the 3n+1 transformation into 3Y+1W with the objective of reducing it to 1 restricted opening square space.

Collatz by Volker Latussek was Hendrick Haak’s exchange puzzle at the International Puzzle Party (IPP) 41.  It consists of 3 Y pentominoes and 1 W pentomino.  The objective is to place all 4 pentominoes in a 5x5 square.  To help you do this, a 5x5 tray is provided.  To further help you, there is a top on the tray to keep pieces from jumping out while you solve the puzzle.  A small slot in the side provides a convenient way to add the pieces to the tray.  Of course it is slightly offset to keep pieces from simply sliding out.

The puzzle is a nicely made ensemble of 3D printing and Laser Cut Acrylic.  The tray is 3D printed and the 4 pieces and top are laser-cut from Acrylic.  The top has 4 sizeable holes that can be used to manipulate the pieces within the tray.  And it can be slid off so that you can easily store the pieces in the tray so that they don’t fall out.  I came to the conclusion a while ago that all the packing puzzles that I print would have a sliding opening and I’m glad to see others embracing this as well.

So my solving experience went like this: This looks like it might work but I’ll be disappointed if it’s that easy.  Nope, the offset opening doesn’t allow that.  OK – maybe it’s like this, but it would still be too easy.  Nope #2.  Maybe I should think about it for a minute.  How about this – Yup.

It’s not difficult, but you do need to determine how the pieces interact with each other to get them correctly into the tray.  And I wasn’t disappointed!

Puzzle Philosophy - Yin Yang

I like puzzles but they aggravate me.  When I’m working on a puzzle, I can’t wait to find the solution.  When I find the solution, I’m disappointed that it’s over.  I expected all these reoccurring conflicting emotions to surface when I pulled (pushed?) Yin Yang out to work on.

Yin Yang was developed by Volker Latussek and made by Pelikan Puzzles.  The box was made using Cherry and has a Maple (Yang) top to contrast nicely with the 6 Wenge (Yin) pieces.  When all the pieces are packed in the box, you end up with a nice digitized taijitu symbol.

Upon inspection, 4 of the Yin pieces are symmetric and the other 2 are not.  These asymmetric pieces are the key Yin and Yang pieces.  I know that I stated that the Wenge pieces were the Yin to the box’s Yang, but even when you separate them, you still have both in each.  Yeah, it doesn’t make a lot of sense, so let’s just agree to call it a principle and keep building on it.   Now that we have our key Yin Yang Yin pieces, as long as they aren't symmetrically situated within the assembly, these mystical keys can be used to affect a transformation between Yin and Yang assemblies.  You’ll also notice that extra effort went into highlighting that each piece was constructed by combining a 2x3 block with a 1x2 block.  I suppose one of those would be the Yin and the other the Yang requiring the key pieces to be formally referred to as the Yin Yang Yin Yang Yin pieces.

Yin and Yang

Since the Yang box encompasses a 4x4x3 space, the objective is to 1) Find a way to make a 4x4x3 shape with the Yin pieces and 2) discover a method for jamming those Yins into the Yang.  And the answers to all your questions are Yes – Are rotations allowed/required, Are there uncrammable assemblies, If I Yin instead of Yang will the pieces get stuck?

I’m embarrassed to admit it took longer than expected to find a 4x4x3 assembly.  Of course once I found it, it had to be the required assembly and I was never going to let it go.  I could see how the first 3 pieces would come out and only had to figure out how to release the remaining 3.  Surely, taking out (Yang?) / putting in (Yin?) 3 pieces with all that space couldn’t be that hard (With all my experience with 3D apparent packing cubes, it’s a wonder I can still think that).  Needless to say, I spent a considerable amount of time experimenting with some amazing cramming techniques with those obstinate pieces until I remembered the principle of the whole thing and immediately solved it.

Off With Her Head! - Guillotine

AAAGGGHHHHHHHH!!!!!!!!!  Off with her head!  The only puzzle that I left unsolved at RPP that tormented me was Guillotine (aka Harun) designed by Volker Latussek.  Just when I thought that I had left all that stress behind me, a package arrived from the UK.  Allard Walker, somehow sensing that I would be starting to recover from my traumatic experience at RPP, strategically mailed me a copy to arrive just in time to prolong the frustration.  I’m lucky to have such good friends.

It turns out that Guillotine was Allard’s exchange puzzle for the Edward Hordern Puzzle Exchange at IPP39 this year.  For those not familiar with the exchange, each participant brings up to 100 copies of a new puzzle design that has not been released in the wild yet, to exchange with the other participants.  This year there were just over 70 participants, so each participant left with 70+ new puzzles.  In addition, a copy of each puzzle is donated to the Lily Library at Indiana University, which now houses more than 34,000 puzzles, generously donated by IPP's founder, Jerry Slocum.

As I explained in A Decade of Puzzling – RPP 2019, when I got back from RPP, I had an epiphany on how to finally solve this bugger.  Overjoyed to finally be able to validate my hypothesis, I eagerly unpacked Guillotine and began to arrange the pieces.  Unfortunately, epiphanies are cheap and this one wasn't worth much.  It wasn't even close.

Guillotine consists of 12 pieces that have to be packed into a 5x5x5 box.  There are 6 planks that are 4x2x1 and 6 additional 4x2x1 planks that have 2x1x1 pieces added on each end (or you can think of it as a 4x2x2 burr piece with a 2x2x1 notch taken out of the middle).  The box has a sliding lid that covers half the box.  It only covers half to allow the pieces to stick out in the unsolved state that it comes in.

After giving up on my erroneous hypothesis, I called it a night to get some sleep before attacking it again.  I resumed the effort again in the morning, and after a short time finally managed to find a solution. Very clever puzzle!

Peter Wiltshire mentioned that there were 2 solutions at RPP, a hard one and an easy one.  I assumed that after all the struggling that I did, I finally managed to find the easy solution.  After another 5 minutes, I found the second solution.  Having both solutions, I’m now assuming that I found the harder one first and that’s why I found the second solution so fast after the first one.

The copy that I played with was made by Eric Fuller and went by the name Harun, which I assume is the name that Volker Latussek gave the puzzle.  Allard’s exchange puzzles were made by ROMBOL GmbH, and I’m told that they sometimes change the names of puzzles for marketing reasons.  So Harun became Guillotine.  Either way, this one is a tough one to get your head into, or maybe I should say out of.

Thank you Allard!