How many different types of love are there? According to C. S. Lewis there are apparently 4: Storge/Affection, Philia/Friendship, Eros/Romance, and Agape/Charity. Can you hold all this love in your heart at the same time. Hanayama seems to think so. The Huzzle Cast Arrows puzzle has a heart with 4 arrows stuck in it, one for each of the types of love.
I attempted this puzzle at last year’s RPP and didn’t have a chance to solve it. I wasn’t planning on getting my own copy, but since I was placing an order with Puzzle Master for the Puzzle-A-Month Challenge , I added it to my basket.
No matter how the arrows are moved around, and it is a pain to get all 4 arrows where you want them in the orientation that you want them, it just doesn’t seem possible to extract them. Do they come out at an angle? Does more than one come out at a time? Is there some kind of coordinate motion required? How can the shape of the cutout in the heart be exploited? These are just some of the typical questions that arise when struggling with this supposedly simple Level 3 Hanayama puzzle. Personally, I’d rate this one at Level 4.
Although files, pliers, and blowtorches may be included in your puzzle solving kit, there is a solution that does not require any force or external tools. When you have figured it out and know what to look for, it’s not that hard to remove and return the arrows from the heart. Once it’s apart, it’s easier to see exactly how it works without all the arrows flopping around. The solution is easily repeatable and you can play Cupid all day to your heart’s content.
What I like the most about this puzzle is that it is a great application of the Reuleaux Triangle. A Reuleaux Triangle is 2D shape that has the same width regardless of its angle of rotation. You can make a Reuleaux Triangle by taking an equilateral triangle (all sides the same length), and using a compass oriented at each point to connect the other 2 points with an arc that has a radius that is equal to the length of the side of the triangle.
The heads and tails of the Hanayama arrows appear to be based on Reuleaux Triangles and the opening in the heart with the other arrows in the way is just a wee bit smaller than the width of the Reuleaux Triangle. I leave it to you to figure out how to get past this paradox.
Wednesday, August 28, 2019
Wednesday, August 21, 2019
Every year, shortly after IPP, several puzzlers converge on upstate New York to have a picnic. This year’s Rochester Puzzle Picnic was held on 17 Aug 19. Since some attendees travel 6 or more hours to attend RPP, people usually start to arrive on Friday and depart on Sunday in order to dedicate the entire day on Saturday to puzzling. That’s a lot of picnicking!
At some point during the course of the weekend, we realized that this was the 10th annual RPP. Our gracious host for 10 years in a row has been Jeff Aurand, who allows a motley crew of puzzlers bringing large quantities of puzzles into his lovely home for this grand puzzle extravaganza. Vast quantities of food, vast quantities of drinks, and vast quantities of puzzles. What could be better!
Friday is always a lot of fun catching up with friends, some of which we haven’t seen in a while, and setting out puzzles for everyone to enjoy. This year, a table was set up with some of the puzzles that were in the IPP Nob Yoshigahara Puzzle Design Competition. Competition puzzles that were at RPP include:
Cast Slider by Vesa Timonen – Normally we see some of the design competition entries become Hanayama puzzles. This is a case of a Hanayama puzzle becoming a design competition entry and it was a top 10 vote getter in the competition. The object is to slide the two main pieces off the central holding piece. However, they seem to get caught at the end. Although this puzzle is rated by Hanayama as 3 out of 6 stars, it provided a challenge for several people that tried it.
Cover Up by George Sicherman – Four pentacubes required to completely cover a tetracube. The version put out to play with was made by myself for others to play with. I didn’t find out till later that Brian Menold had much nicer versions on hand for sale that we could have put out instead.
Outstandin' by Haym Hirsh – Haym has been putting out a flurry of packing problems for acrylic boxes. This one is a ball packing puzzle with 3D printed pieces.
Multiball by Eric Fuller – Eric has recently stated that he will be developing many new puzzle boxes for the puzzle community. Multiball is the most recent of these and someone was kind enough to bring theirs for others to play with. This also sparked some conversations on the “official solution” vs another solution found by others.
Triagonal Pyramid by Kohno Ichiro – 4 pieces with 2 half cubes each that make a triagonal pyramid. Of course, this sparked a debate of what a triagonal pyramid was. I brought a homemade copy of Triagonal Pyramid for others to play with, but it lacked the magnets that help hold it together. I justified not adding the magnets since I didn’t know the polarity orientations used for the design. However, if you acquire a copy of your own, make sure it has magnets.
Petit Ring by Osanori Yamamoto – Osanori has been making many interesting restricted opening packing puzzles and this was also one of the top 10 vote getters at IPP39. You only have to pack 3 pieces in a restricted opening box, and has TWO openings!
Standing Egg by Osanori Yamamoto – The goal of this puzzle is to make a cube with one missing corner that can stand upright on the three points that result from the missing corner. The one at RPP was beautifully made by Tom Lensch.
Somaa Cube by Haym Hirsh – Haym has been designing a lot of Soma varients and Somaa is one based on using non-cubic rectangular parallelepipeds (or in English – cubes stretched/compressed by different amounts in each direction) to make the Soma-like pieces. I believe that the X, Y, and Z dimensions of each of the blocks used to make the pieces are 1 of 3 values. Since 3^3 is 27, I would guess that there is one block for every possible combination of measurements. The Somaa Cube was made by Brian in a variety of exotic woods resulting in beautiful pieces and an even more beautiful cube once it was all put together.
TD345 by Chico Banan – This puzzle was described in the prior post, Chico Strikes Again. Somehow Jeff managed to score one of the 2 copies that were made for the IPP design competition and, as expected, it was highlight of RPP 2019! Enough said.
Tetra Spinner by Yasuhiro Hashimoto and MINE – This is a clever constrained packing puzzle with 2D tetra pieces sandwiched between 2 plates of plexiglass. Each piece is a different color to help easily identify the individual pieces as you insert them in and move them around in the frame.
In addition to these puzzle design competition entries, there was a large assortment of other puzzles brought by everyone, strewn upon the horizontal surfaces of Jeff’s living room, to entertain everyone. Puzzles that I managed to solve that first night include:
Hat Trick – As previously mentioned, this puzzle, designed by Laszlo Molnar, was a top 10 vote getter in the IPP39 design competition. After the competition entries were released before IPP started, I studied the entry online and worked out in my head how the solve would go. Presented with the actual puzzle, I was able to verify my approach and quickly determine that I had accurately imagined it. However, the actual puzzle was much more beautiful than my intangible copy. Brian did a fantastic job making these and I took one home with me!
Petit Ring – If the IPP wasn’t tired of giving Osanori Yamamoto awards, this one would have probably received one. Only 3 simple pieces that have to be inserted within the frame such that each opening in the frame was completely filed. I really enjoyed working on this one. Not too difficult but a nice challenge. Tom made this beautiful copy.
Somaa – You used to be able to refer to someone’s Soma variant by saying the designer’s name and Soma Cube. Haym has ruined that approach by recently releasing several Soma Cube variants plucked from the Somaverse. I didn’t find this puzzle overly difficult. I convinced myself that I was following a reasonable procedure for deriving the solution that was a combination of identifying the best size block faces to match along with some backtracking. Of course, I could have just been lucky. Brian made the beautiful copy that was at RPP and I’m guessing that they will be available again at Wood Wonders in the near future.
Mushkila – I’ve seen several references to Yavuz Demirhan’s Mushkila puzzle on Facebook and was looking forward to trying this one. 5 elbows and 1 straight piece packed in a constrained opening box. This one is not that difficult and a good puzzle for new puzzlers. The version at RPP was beautifully made but I don’t know who made it.
Wavelinks - Rod Bogart entered Wavelinks in last year’s IPP design competition and was a Top 10 vote getter. When I saw it in the competition room, I thought that the design was brilliant. I successfully took it apart but the room was closed before I could get it back together. Now a year later, I had some more time to focus on it. As with last time, I was able to quickly separate the red and blue rings and marvel at the motion required for separating them. It was also easy to make separate red and blue rings that weren’t intertwined. When I thought I had it all figured out and set the assembly into motion, I discovered that I had 2 red and blue intertwined rings. A little tweaking, and I was back to a red and a blue ring that were intertwined. The motion is so mesmerizing that I played with it some more and determined that there is more than 1 way to start the assembly process, with some easier than others. A year later, I still think this is a brilliant puzzle and I hope that Hanayama will carry it sometime in the future. It would look fantastic in 2 contrasting metal finishes.
Tetra Spinner – After seeing this in the list of IPP39 design competition entries, I was looking forward to playing with it at some point. It looked like an innovative approach to a restricted 2D packing problem and the IPP39 participants agreed, making it one of the top 10 vote getters in the competition. I enjoyed working on this one. It is fairly straight forward and doesn’t really require a lot of convoluted moves.
In between all that puzzling and talking, eating was also another popular activity. Jeff grilled up some vegetarian and chicken shish kebobs that he and Sue skewered up. It was accompanied by an excellent rice dish. Jeff is an awesome chef and you could easily go there just for the food.
In addition to all the puzzles, a big thank you goes to Brian for bringing Wood Wonders T-shirts for everyone.
The main day had arrived and we started it with some fresh bagels and cream cheese that Jeff went out and procured. After caffeinating up, it was on to puzzling and other related activities.
Every year, there are some breakout sessions involving multi-person games. This year’s game, Unlock! Exotic Adventures – Scheherazade’s Last Tale, involved lots of team puzzle solving. The game incorporated a cell phone app that contributed a background theme song to accompany the cards being used. Its always fun listening to banter that accompanies the games progression.
Another of the RPP highlights every year is the Peter Wiltshire magic show. This year’s performance featured a beautiful box with 3 die, made by Peter. He’d show the 3 die in the box, put the cover on, and shake it so you tell that they were all in there. Then he could pull one out and then shake the box to verify that one was missing. Then magically, the dice would appear or disappear from the box as Peter showed it to the spellbound crowd accompanied by gasps of “I can’t believe it”.
For lunch, Jeff barbecued some hamburgers, sausages, and chicken, Tom made a salad, and I made some guacamole. That along with some other salads kept us going for the rest of the day. Of course, most people brought some type of dessert, so there was plenty of that as well.
Another tradition of the RPP is the John Rausch give-away auction, where John brings puzzles that need to move on to someone else that can use them. The collection of puzzles are displayed on a table and everyone picks a number from the hat. People then take turns selecting a puzzle from the collection based on the number picked. Since there were more puzzles than puzzlers this year, there were multiple rounds of selections. I ended up with some very nice puzzles this year and applaud John for his generosity and the fun that it provides.
During the day, I was able to tackle and solve several puzzles including:
XTic – Andrew Crowell part 2. This was the second of Andrew’s puzzles, beautifully crafted by Brian, that he brought along. This one was a lot of fun and I enjoyed the rotations and how the pieces traveled through the cube. Andrew may be fairly new to the puzzle community but he has quickly dominated the Turning Interlocking Cube category. I’m always looking forward to new designs that he has coming out.
Cluster Buster – Brian brought a prototype of Cluster Buster designed by Rex Dwyer that he made in Catalpa . This puzzle is a Coffinesque geometric shape consisting of 6 pieces that is so intimidating that Brian brought a solid example of the final shape for reference. Some of the deep triangular pockets are displayed on the outside while others get filled by points from other pieces. I managed to solve this one, using experience from solving Coffin puzzles and a bit of luck. It’s a very nice design and I’m assuming that Brian will be providing these in the near future.
Half Lid Box – This beautiful puzzle, designed by Hajime Katsumoto, was made by Made by Eric Fuller and sold on Cubicdissection a year ago. Although, I found this puzzle fairly simple, others had a more difficult time. Sometimes you just get lucky!
Rectilinear – Tom brought a prototype of Goh Pit Khiam’s Rectalinear puzzle to get some feedback. He brought a copy of the 4x4 board and a description of the puzzle including what the pieces looked like. He apologized for not bringing any pieces, but that didn’t stop us from making some from cardboard. The goal is to make a complete circuit between an identified source and destination using all the pieces with all the lines part of a single circuit. It reminded me of Tom Cutrofello’s Lab Mice puzzles. I could easily see this type of puzzle expanded and picked up by a company like Thinkfun. For so few pieces, I found the challenges more difficult than I expected. Unfortunately, I cannot provide any photos that would not give away the puzzle design.
Pack 3 – This my favorite of Osanori Yamamoto’s packing puzzles made by Tom that I played with during RPP. For only 3 pieces, I ended up spending quite a bit of time finding the solution to this. It required an interested sequence of movements to get those 3 pieces in position and I liked it a lot. If you could only get one of Osanori’s packing puzzles, I’d recommend this one.
Cribbage Dance – Puzzle gatherings like RPP are a great opportunity to get feedback on new puzzles and Tyler Somer took advantage of this by sending 2 copies of his Cribbage Dance puzzle for people to try. Tyler also pointed out certain issues that he was not happy with, and was soliciting potential solutions to what he considered a problem. Needless to say, several puzzlers reviewed the puzzle and provided feedback, not all of it happy/glad/good job tidings. The puzzle consists of a frame with 3 sliding plates and 2 burr pieces running through the plates. On first glance, it looks like it would be extremely difficult. When I see these types of puzzles, I assume that the difficulty goes up exponentially with the number of plates and the number of burr pieces. 3 plates is a warning for me and I usually don’t buy these types of puzzles with more than 2 plates. However, in this case, all the plates are the same and their orientation is obvious, taking that out of the equation and putting this puzzle in the easy category as opposed to the hard category on my personal scale. The puzzles were nicely crafted by Greg Davis.
Die Welle – Rich scored this Jean Claude Constantin N-ary puzzle from John’s auction. I decided to go through the motions of moving the balls from the starting point to the ending point. Not difficult, but a nice fidget type puzzle. I though the best part of the puzzle was the design of the holes at the beginning. The plexiglass is cut so that there is a springing movement to it, allowing you to push the balls in, but keeping them from popping back out. Very clever!
Kawashima W Box – You would think that from the puzzle descriptions, that RPP is a burr/packing puzzle party. Au contraire, there are serious puzzle box aficionados in attendance at RPP including the host himself. The only box that I tackled was the W box by Kawashima. Not very difficult, but the craftsmanship was very good.
I wound up Saturday night by trying to solve the Harun Packing Puzzle by Dr. Volker Latussek. This puzzle was made with Black Limba and Zebrano by Eric Fuller at Cubicdissection. It consists of 6 identical 2x2x4 notched pieces and 6 identical 1x2x4 boards. The object is to pack a 5x5x5 box with no internal obstructions and I was told that it has not 1 but 2 solutions, one supposedly hard and the other easier. It looks quite simple but I was unable to obtain either of the solutions, unless one of the solutions is to leave a piece out. I packed it in, myself not the puzzle, at 1am to get a few hours of sleep before attacking it again.
SundaySunday morning, the topic of drilling square holes came up and Jeff took us out to his workshop to give an impromptu mortising demonstration. I always like to go out and spend time in the shop even if it is only to look since Jeff has a very nice setup. While walking around the shop, Jeff ran across some rejects of his Reversal of Fortune Box for the Apothecary Chest. Of course, the term reject is relative and what Jeff considers a reject is leagues beyond what I can make on an exceptionally good day.
After some collaborative brainstorming, Jeff gave some of these non-operational copies a quick pass on the table saw to transform them into functional puzzle boxes at the cost of a slightly shortened top. A few people were more than happy to take home a slightly modified and unfinished version to enjoy the wonderful mechanism of this unique and extremely limited puzzle box.
While sitting around chatting with the other puzzlers, I started to play with a copy of Bouquet by Christoph Lohe and made by Brian. I didn’t have enough time to get too far into this one, but at 23 moves to remove the first piece, I’d have to dedicate some time to focus on this one.
I also spent quite a bit more time trying to find the solution to Harun without success. After returning home, I had an epiphany and think that I know what is required to solve it. Of course, epiphanies are cheap and I’ll have to wait for another opportunity to test my theory.
I brought a new puzzle that I designed after IPP called Broken Soma. Several people tried it and 1 person was able to solve it. Brian will be offering copies on Wood Wonders in the near future.
You may be thinking that this gathering is all about puzzles, but in reality, it’s all about the people. That’s what makes it all worthwhile. So find some people near you and have your own puzzle party!
Wednesday, August 14, 2019
This was once again confirmed with Quadripole from Wood Wonders. It was designed by Stéphane in 2012 and made by Brian in 2018. It is a level 22.214.171.124 puzzle consisting of 4 pieces captured within a frame. The objective is to remove the pieces and then reassemble them back into the frame. The puzzle is beautiful with Pink Ivory pieces and a Catalpa frame.
There are several things that I like about the design. The first is the simplicity of the frame. There are no additional fixed cubes blocking movement within the frame. It is the same on all sides, so the orientation of the pieces to the frame doesn’t make a difference. I consider this more elegant than frames that have internal obstructions added to increase the level of difficulty. I also like how the puzzle only has 4 pieces that get inserted within the frame. It makes it seem innocuous with only 4 pieces (some puzzlers never learn).
Some of you may be saying to yourself: that puzzle was released by Wood Wonders a year ago, why is he blogging about it now? There are several reasons for that and here is the short version of that story. After ordering the puzzle, it joined the backlog of puzzles to be solved. I have 2 types of puzzles in my collection: those that have been solved and those that have yet to be solved. Both sides of my collection seem to be expanding.
Shortly after receiving the puzzle, Brian sent out an email indicating that one of the pieces may be missing a cube and if it was, he would send a replacement. Very kind of Brian to offer to make the puzzle potentially more difficult than it already is. This is why I like dealing with people like Brian. Not only do you get quality workmanship, but he stands behind his work. This prompted me to take the pieces out and examine them and sure enough, I was missing that extra cube.
After receiving the updated piece, the unassembled puzzle sat on a shelf in the dinning room for several months. This is not unusual in our home since I like to disassemble puzzles and let them sit for a month or 2 (or 3 or 4 or 5 or … you get the picture) to provide enough time to forget anything that I may have learned from the disassembly process. For Quadripole, I successfully remembered nothing!
After enough brain cells died off, I sat down for several hours on several occasions attempting to get this puzzle back together. Normally, when working with the pieces, I get a sense of how they interact with each other and can put those working relationships together to form a solution. For instance, one of the pieces could only exist within the frame with 2 orientations, so there were only two sets of potential solutions to search through.
Unfortunately, I was unable to uncover the solution by examining the piece relationships and had to resort to a brute force look at all possible piece position/orientation combinations. While doing this, I discovered some potential relationships that I have not noticed before and soon had the pieces back in the frame. Solved!
But wait a minute! It felt like one the moves that I used near the end, may have required a little tilting motion to insert the final piece. It was so minor that I checked it several times to convince myself that it was indeed a rotation. I didn’t remember seeing any reference to a rotation and checked the box that the puzzle came in. The nice thing about this box is that Brian included a label with a picture of the puzzle along with a description. Sure enough, no reference to a rotation. I also noticed that the label indicated that it takes 22 moves to remove the first piece and I didn’t feel that it took me that many moves. Sure enough, I checked my solution and not only did it have a rotation, but it only took 14 moves to remove the first piece.
It turns out that I stumbled upon the secret 2nd solution only encountered by the mystic puzzlers of …. After I finished daydreaming, I plugged the puzzle into BurrTools to verify the stated 126.96.36.199 difficulty, and sure enough, it was quickly validated.
In the end, it looks like there are 2 solutions to Quadripole; a level 22 rectilinear solution and level 14 rotational solution. I would have preferred that there wasn’t a second solution, but to be honest, I was in need of some level of accomplishment when I stumbled upon the rotational solution.
Thanks again to Stéphane and Brian for another fine masterpiece!
Quadripole II?After putting Quadripole back together, I felt compelled to pull the Beta Funzzle puzzle out of the to-do pile since various references have indicated that Beta, designed by Mr. Y Gong, is similar to Quadripole. Puzzle Master, the exclusive distributor of Beta, indicates that it is a variant of Quadripole on their website.
Funzzle Beta is made from Bamboo and is attractive enough. Puzzle Master rates it at a level 10, which is highest on their level of difficulty and well deserved.
So how do the designs for Quadripole and Beta compare?
|Quadripole (left) and Beta (right) Frames|
|Beta (left) and Quadripole (right) Pieces|
Complexity – As already mentioned, Quadripole has a complexity of 188.8.131.52, while Beta has a complexity of 184.108.40.206! (No, that’s not a factorial). That’s an impressive amount of moves to take out that first piece and it is an amazing process to go through.
Overall Design – I found the Quadripole design attractive due to the elegance of its design and at level 22, I believe that it is approachable to a large segment of the puzzle community. Beta on the other hand trades elegance for complexity, but Oh what an amazing dance it provides. At level 43, it may be out of the reach of many but well worth watching in Burr Tools.
I can’t recommend the mass marketed Beta puzzle because this Funzzle was not fun. The pieces were fiddly and attempting to move them around was just frustrating. I quickly gave up trying to solve the puzzle and entered the puzzle in BurrTools. Even following the steps with BurrTools was frustrating with the quality of the pieces. However, if a nicely working version ever becomes available, it may be well worth acquiring.
You can read about Kevin’s take on Beta here and Gabriels impression here.
Wednesday, August 7, 2019
Chico’s entry in the recent Nob Yoshigahara Puzzle Design Competition was TD345. This puzzle was the buzz at the competition and it was inevitable that it would be on the tip of everyone’s tongue.
This awesome puzzle was the overwhelming favorite in the competition and garnered the most votes of any puzzle in the competition by far. In fact, it received so many votes that the vote counter rolled over and mistakenly put TD345 in last place. Unfortunately, this oversight was not discovered until after the awards ceremony but Chico is looking forward to his trophy.
|TD345 with SPH|
The TD345 prototype used rivets to connect the TDs, but at the last minute, Chico decided to use fasteners to give the puzzle competition participants the opportunity to satisfy their urge to rip them apart. His thoughtfulness towards frustrated puzzlers knows no bounds.
Chico vehemently denies that his flat articulated chains were influenced by the movie Snakes on a Plane although rumor has it that you could hear the puzzle design competition participants occasionally quoting the movie: “I have had it with these mothaf…ing snakes on this mothaf…ing plane!”
With this puzzle design entry, Chico has finally and definitively proved that the TD complete problem, “Does 32 + 42 equal 52,” is indeed true as most people had come to believe (even Pythagoras!).
When asked what his next project would be, Chico humbly said that his vision is to inspire others to fix the Soma cube.
As a final warning, please do not put the TD345 puzzle in your mouth! You think that this would have been obvious, but there were several sightings of purple tongues at IPP this year.
Many thanks to the Chico Banan fan club that unknowingly submitted the photos used for this post.