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.

Stuffing Puzzles – Xmas Stocking

I’ve seen references to the Xmas Stocking puzzle recently that caused my mind to wander a bit.  Since all the pieces were identical and packed in a fairly small box, I was wondering if I could solve it without having the puzzle.  After several minutes of determining how the pieces would need to be oriented due to the opening and rotation restrictions, I was able to visualize some assemblies but not how the pieces could be placed in the box.  I eventually resorted to using a piece of paper to map out the possible assemblies with no further luck.  It’s possible that this is one of those puzzles that requires some assistance like larger tolerances or beveling.  I was about to move on when I remembered that I had received some LEGOized hand-me-down puzzles from a generous soul on the Mechanical Puzzle Discord (MPD) server and sure enough, there it was.

Xmas Stocking is a 3D restricted-opening packing puzzle designed by Osanori Yamamoto.  It consists of 5 identical Z tetracubes that have to be placed in a 2x3x4 box with 2.5 voxels on the top closed off.  The triangular half-square is there to restrict pieces from moving through that square while forcing the voxel underneath to be occupied – assuming that the opening needs to appear completely filled.  I was unable to find verification of that requirement, but these types of puzzles seem to require that and it turned out to be the case for this puzzle.

Most of the 3D LEGO packing puzzles that I recently received came solved.  However, since they are made from LEGO bricks, you can simply rip off the bottom and dump the pieces without seeing how they are arranged or how they come out.   The LEGO bricks used to make the box also included portholes to view the interior of the box, but they are not needed to solve the puzzle.  

Being made from LEGO bricks, you know that there are no rotations that can occur with loose tolerances or bevels unless very specific pieces are used or they are doctored in some way.  Armed with that assumption, I tested the pieces and could get no further than my pencil and paper analysis.  Yes, of course I realized that I was operating with a bad assumption somewhere but was having a difficult time identifying what it was.  And then I dropped a single piece in the box and it bounced it’s way into an orientation that I had thought was impossible.  Apparently, the Z tetracube has a nice property that gives it a possible rotation that I had not thought of.  Now that the secret was out, it only took a couple of minutes to get all 5 Z tetracubes nestled within the box.

I don’t know if it was intentional, but the LEGO version did have the interesting property of still being apparently filled even with all those holes.

Mail Call

King Of Red Herrings – Neptune

Neptune is a 3D packing puzzle designed by Osanori Yamamoto and made by Pelikan Puzzles.  The pieces are made from Maple and contrast nicely with the Mahogany box.  The box is very well made and has the name of the puzzle and designer identified on one of the sides.  The box also features 2 large opposing slots in the box for entering and manipulating the pieces.

I was a bit surprised that the puzzle consisted of 6 pieces to be packed within the box.  This is more than you would typically encounter for this type of puzzle, especially from Osanori.

I assumed that the goal was to make an apparent cube within the box.  Taking the 6 pieces, I was quickly able to make a cube outside the box.  It took me a minute to realize that it wasn’t just apparently a cube, it was a cube.  All 27 voxels of the 3x3x3 space are occupied.  I was completely surprised since that would mean that the first piece to be removed would have to come out in a single move.  Completely un-Osanori like.

So I did some googling and found a couple of reputable sites indicating that the level of difficulty for Neptune was 7.2.1.2.2.  This means that the first piece would come out after 7 moves.

What!!!  That’s not possible!  I’m certain it’s not possible.  It couldn’t really be possible could it?  Will this puzzle open my eyes and demonstrate some out-of-this-world physics to accomplish the seemingly impossible?

Taken in by this claim, I spent an hour revisiting my assertion that the first piece must come out in 1 move and tried to find a flaw in my logic that would allow a move that did not free the first piece.  Try as I might, I was unsuccessful and decided that something fishy was going on.

Starting over with the assumption that the first piece comes out in 1 move, I rather quickly had the pieces packed within the box.  It wasn’t that difficult.  Most of the time I had spent with the puzzle was trying to envision the impossible.

So did I really solve it?  I believe so.  I dug a little deeper and found that puzzlewillbeplayed.com had the same level that I experienced – with the first piece coming out in 1 move!  I should have checked there first.
 

Two Lips Are Better Than One – Tulip 1

What do you call a puzzle with a large square corner opening that incorporates 2 lips constructed from triangular half-squares?  Perhaps 2 Lips or maybe even better Tulip.  And if there is more than one design like that, maybe they can be called Tulip 1 and Tulip 2.

Tulip 1 was designed by Osanori Yamamoto in 2019.  It is a 3D apparent cube packing puzzle where the objective is to assemble 3 pieces within a frame such that there appears to be a 3x3x3 cube within the frame although there may be unseen holes within the frame.  Spoiler/No Spoiler – there are vacant voxels when the pieces are packed in the frame.  The frame has a very large and very obvious open corner to add and remove pieces and a single voxel opening in the opposite corner.  My version was made by Pelikan with a Padouk frame and Wenge pieces.  It looks and feels fantastic and is a fun little puzzle with 13 moves to take the first piece out.  Of course, since I consider it an assembly puzzle, it’s really 13 moves to get the last piece in.

As already mentioned, the large opening in the frame has 2 lips.  Why is this of interest?  I would argue that each lip makes its corner open so that the adjacent internal voxel needs to be occupied to satisfy the apparent cube criteria while at the same time being closed so that pieces are barred from being removed there.  Open and closed.

To solve Tulip 1, my initial attempt was to find an assembly of the pieces that would fit within a 3x3x3 space but I ended up with too many assemblies that obviously wouldn’t satisfy the apparent cube requirement.  So I looked for assemblies with a solid corner to fill the large opening while simultaneously having cube in the opposite corner to fill the smaller opening.  This didn’t quite do it for me either, so I instead focused on ways to use the smaller opening.  Now sure, that opening could be there just to force a cube in that corner but I was going on the premise that one of the pieces would eventually have to stick out of that hole.

And thus I found a good candidate assembly that permitted a nice sequence of a few moves.  And if I’ve learned anything from these types of puzzles, if it makes a few nice moves, it’s probably the start of the solution path.  There were a couple of times that I thought I had it solved but there was a move in my path that was not realizable when actually in the box.  I could get it to what I estimated was the half-way point but I couldn’t free the first piece.   Eventually, I realized that the first piece to be removed was not the one I was trying to liberate.  With that new perspective, I completed the solve.

Tulip 1 is another great puzzle from Osanori.  Now to track down Tulip 2.
 

Apparently Aesthetically Pleasing – Belt Cube 3

Pelikan Puzzles has made quite a few clever apparent cube packing puzzles designed by Osanori Yamamoto.  I’ve already talked about W-Windows and Pumpkin 1.  Now let’s look at Belt Cube 3 released in 2019, although I only recently acquired this copy.

Belt Cube 3 is a very attractive puzzle made with a Purpleheart frame and Wenge pieces. With only 3 pieces and a wide open frame, how difficult could it be?  Technically, it has a 10.2 level of difficulty.  This can be loosely translated as fun but not very difficult for this type of puzzle.

The symmetry of the 2 rather large frame openings gives you a big clue as to how the 3 pieces need to be assembled to make an apparent cube.  And yes, there apparently is a non-apparent configuration.

When I started working with the pieces, I quickly found a configuration that looked promising but was having difficulty figuring out the moves required to get it in the frame.  However, having learned my lesson (many, many, maannnyyyyy times) I stuck with it until eventually the pieces appeared to make a cube within the frame.  For puzzles like this, it’s all about appearances.  My rule of thumb for this type of puzzle is if you find a configuration that supports at least 3 to 4 cool consecutive moves, it’s probably the solution and there is a 5th move, and a 6th move, etc.

I found this one a bit easier than the others that I have done, but to be honest, you can’t go wrong with any of them.  They are well made, beautiful, and apparently aesthetically pleasing.

Some Puzzles Give You The Shutters – W-Windows

Provided: Box with 2 large windows and 3 escaped pieces.  Your Mission (should you choose to accept it): Contain the pieces and shutter the box.  That’s shUtter the box, not shAtter the box, no matter how tempted you may be mid-solve.  As always, should you or any or your puzzling buds be caught shAttering the box, we will disavow any knowledge of your actions.

W-Windows is an apparent cube packing puzzle designed by Osanori Yamamoto and made by Pelikan Puzzles.  In this case the box has 2 large 2x2 windows that need to be shuttered (i.e., filled) and 2 of the 3 zig-zaggy pieces have a W theme going on.  The box is made from Apple and the pieces are made from Ovangkol.  Usually, I don’t talk about the types of woods used to make puzzles, but since I had to look up Ovangkol in my wood book (Wood! Identifying and Using Hundreds of Woods Worldwide by Eric Meier from the online The Wood Database), it’s worth mentioning that it’s another name for Shedua.  However, Ovangkol is the title for the wood description and Shedua is only mentioned in the comments.  Apparently Ovangkol is used by guitar makers who have better lobbyists than puzzle craftsmen.

After having done many of these types of puzzles and looking at the pieces for W-Windows, I expected:

• All pieces will be used to fill the windows.
• The W pieces will be added with some variation of an insert-shift-insert movement.  Sorry to state the obvious
• One of the Ws has a 2x2 face, which obviously fills one of the box windows.  It’s so obvious that it can’t possibly be part of the solution.  Or could it?
• The tetracube piece will be in the center somewhere moving around to allow the W pieces to slowly emerge from the box.
• Each W piece will be associated with its own window.
• The tetracube piece will have the highest move count.

I freely share these expectations with you because they are of no help whatsoever when solving the puzzle.

When I first sat down with the puzzle, I took the approach of looking for an assembly and then determining whether it could be placed in the box.  I learned 2 important things from this approach: 1) There are too many assemblies, and 2) There are a lot of ways that the pieces cannot be oriented within the box.  It’s definitely worth the time to determine how the pieces can and can’t be oriented within the box so that you can quickly recognize a possible assembly from an impossible one.

When looking for the solution, I try to find an assembly that looks like it has a few good moves.  These types of puzzles usually don’t have deep false paths, and once you find something that looks interesting, it’s frequently the solution, which was the case with W-Windows for me.

It may be the eternal optimist in me, perhaps the stubbornness, or more likely the short-mindedness, but I looked at the 2 big windows of the box and the 3 measly pieces and thought that this would be a quick score.  However, those simple pieces kept me entertained for about an hour and I did enjoy the solution once I found it.  You really can’t go wrong with these apparent cube packing puzzles from Osanori Yamamoto.  Thankfully, Osanori creates new ones faster than I can acquire and solve them.

Solve Before Midnight - Pumpkin 1

I recently received a Pumpkin that was already cut open with its guts spilled out.  At first glance, I looked at its big carved mouth and 3 simple guts and thought – this is going to be easy.  It wasn’t.  It was surprisingly engaging and entertained me for a considerable amount of time.  I didn’t solve it by midnight and it turned into a puzzle.

Pumpkin 1 was designed by Osanori Yamamoto and made by Pelikan Puzzles with a Pear box and Bubinga pieces.  It is an apparent cube packing puzzle (i.e., the opening of the box is completely filled and any empty space is hidden within the box).

There are a few ways to address the solving process for these types of puzzles.  The first is to find an assembly for the pieces and then test the assembly against the disassembly that is constrained by the opening of the box.  This works best when there are a small number of assemblies.  They usually have a smaller number of pieces as well as a smaller number of voids in the solved cube.  Pumpkin 1’s 3 pieces certainly meet the small number of pieces criteria, but there are 9 voids within the solved puzzle.  Playing with the pieces, there seemed to be a surprisingly large number of ways to assemble them within a 3x3x3 space.  After solving it, I checked with PuzzleWillBePlayed (PWBP) where it indicated that there are 54 assemblies with only 1 of the assemblies provides a working solution.

Another way to tackle the problem is to determine how the pieces can be inserted within the frame through the restricted opening.  However, with Pumpkin 1’s wide open corner, there isn’t much that isn’t allowed.  And yet, it’s not easy to get all the pieces in there as an apparent cube.

At one point, I was hoping that I was correct in assuming that it really was an apparent cube puzzle since I had found at least one solution where all the pieces went in, but there was a visible void.  While we’re talking about making assumptions, I wasn’t aware of the puzzle’s level while solving and was assuming that it took more than 1 move to remove the first piece, which is true for most puzzles of this type.

I finally decided to tackle this particular puzzle by working it from the other end and testing how pieces may move in sequence to release them from the box.  For the first move, does the piece start to come out or does it go further in?  Does 1, 2 or all 3 pieces move together at the same time?  How would that movement allow another piece to move?  Rinse and repeat.

The pieces do allow for some interesting movement.  At one point, I discovered an interesting sequence of moves that seemed to have promise.  Unfortunately it wasn’t the solution I was looking for.  I kept searching for other sequences but couldn’t find anything else even close.  I kept going back to that sequence of moves and tried to find ways to tweak it into submission.  Sadly I couldn’t find anything else.  Even sadder, it was the real solution but I failed to recognize it.  As it turned out, I could have solved it before midnight if I had paid better attention.  That’s the danger of working outside the box.  Sometimes there’s a difference between the virtual world and the real world.

I also learned on PWBP that there are 2 other Pumpkin designs by Osanori – strategically named Pumpkin 2 and Pumpkin 3.  After looking at the other 2 designs, I couldn’t find a similar feature that relates them.  However, Osinori generates so many designs, I can’t blame him for genericizing the naming process.

15 Steps to Success - Stairs Cube

Down the stairs to get a puzzle off the unsolved pile; up the stairs to solve it; down the stairs to put it on the solved pile.  Unlike some puzzle collectors, the majority of my puzzle collection does not reside on the same level of the house where I spend most of my time, requiring me to go up and down the stairs when puzzling.  Who said that solving puzzles wasn’t an aerobic exercise?

After recently going up and down the stairs several times to organize my puzzles, I decided that it was time to take a look at Stairs Cube by Osanori Yamamoto.  This puzzle, made by Wood Wonders, has been patiently waiting for some attention as it listened to the sounds of other puzzles being carried up and down the stairs over the years.  It was overdue to come upstairs and be appreciated.

Stairs Cube is a level 10.3.2 puzzle that consists of 4 pieces.  My version from Wood Wonders is made from Swiss Pear and Wenge.  The 2 woods contrast very nicely and couldn’t be more different.  The Wenge is very dark with a very noticeable grain pattern.  The Swiss Pear on the other hand is very light and so uniform it almost looks artificial.  Together, they make a very attractive puzzle.

If it looks like this puzzle would not be that difficult, you would be right.  It’s obvious where the pieces have to go and pretty easy to get them there.  There are some rotations involved, but they aren’t difficult to navigate.  This puzzle would make a good introduction to burrs requiring rotations.