CrossNeo 3D Puzzle

One more from the capsule ball dispenser. This is the one puzzle I wanted from the set, just to find out what it is. Turns out I had something similar back 6 years ago when Hachette ran their bi-weekly puzzle magazine series. I’m not going to show a photo of the pieces disassembled because that will give away too much of the secret. On a scale of 1 to 3 stars, the puzzle pamphlet gives this one three exclamation marks. Actually, even when I couldn’t remember the original solution, I figured out a way to take this one apart in about 5 minutes. After that, I could solve it in about 20 seconds. Then, I found a video on youtube for something similar, called Cross Sticks, with a much more elegant solution that works within 1 second. Personally, I just like how this puzzle looks when it’s together, and how it feels when I take it apart. Otherwise, it’s not that challenging. (200 yen, 5 cm across.)

Now, for some filler. This capsule ball series has six puzzles: GetaCross, Diamond, Galaxy, PlainCross, Pyramid and NeoCross. That afternoon, as I was doing shopping, I was trying to figure out my odds of getting one more puzzle that I had on my “I want this list,” without getting a duplicate puzzle. At that point, I had GetaCross, Diamond and Galaxy. However, I hadn’t wanted Diamond and I still don’t want PlainCross all that much (after watching the earlier American Woodworker youtube video I kinda want it now, but only kind of). So, what are the odds?

Assuming we have a dispenser with 6 capsules, and each capsule has 1 one of the 6 puzzles in the series, there’s going to be a 1 in 6 chance of getting any given puzzle. So, there won’t be any duplications, but I only want 4 of the 6 puzzles. On the first try, there’s a 2/3’s chance (66.6%) of getting a puzzle I want. After that, the odds depend on the results.

If I get a puzzle I don’t want, then on the next try, my odds go to 4/5 (80%).
If I do get one I want, the odds for the second puzzle will be 3/5 (60%).

That is, if I get a puzzle I want on the first try, there will be 5 puzzles left and only 3 I want. If I get another one I want on the second try, there will 4 puzzles and 2 I want (50%). Then, 3 puzzles and one I want (33%). Finally, I’m going to stop because the odds of getting a unique puzzle that I want will go to 0% (there’s nothing left I want). But, I get all four I want in the minimum of 4 tries, total, and leaving the 2 I don’t want still in the machine.

Conversely, starting with 4 puzzles I want out of 6, the odds of getting one I don’t want are at 1/3 (33.3%). If I get one I don’t want, then I’m left with 1 out of 5 (20%). I get one I want, I go to 1 out of 4 (25%); 1 out of 3 (33%), and 1 out of 2 (50%). So, if I get one I don’t want on the first try, my odds of getting the other one I don’t want before getting the last of the ones that I do, get much worse. I’ll probably have to get all 6 puzzles then, for 6 tries total. The odds favor my having to get 5 puzzles.

If I mark the pattern as “O” = I get one I want, and “X” = I get one I don’t:

X’s in the last two columns means that I only have to buy 4 puzzles then I stop.
An X in the last column means that I have to get 5 puzzles, then stop.
Otherwise, I have to buy all 6 puzzles just to get the 4 I want. From this chart, it’s easy to see that my odds of only buying 4 puzzles are 1/15 = 6.6%. Buying 5 of the 6 are 4/15 = 26.6%, and getting all 6 just to get the 4 I want are 10/15 = 66.6%.

Now, if you’ve been following this blog, you’ll know that I got the Galaxy, then the Diamond (don’t want), GetaCross, and CrossNeo. This just leaves PlainCross and Pyramid. I want Pyramid, but I’ll tolerate PlainCross. So, I don’t really lose anything if I get both of them on my next two tries. I may talk myself into buying all 6 puzzles, anyway.

Now, all this presupposes that there are only 6 capsules and they’re all unique. This is a risky assumption, because 1) I know that there are more than 10 capsules in the machine; 2) I have no way of knowing if the shop staff restock the dispenser overnight; 3) I have no way of knowing if I’m competing against someone else who is also getting these puzzles; 4) I have no way of knowing if the guy that originally stocked the machine filled it with an equal mix of each of the puzzles and if they’re in the machine randomly or not.

Say I’m the only one interested in these puzzles, that they were evenly mixed and random, and that there were 36 capsules in the dispenser at the start. The odds get much worse. 36 capsules, six each of six puzzles – on my first try, my odds of getting one I want are 4 in 6, or 66.6%. BUT, after that, regardless of which puzzle it is, there will still be 5 of that type, increasing my chances of a duplication to almost 100%.

On the first try, I get one I want. Now, it becomes one I don’t want because I’ll have two of the same kind and that’s an undesirable outcome. 5 + 6 + 6 I don’t want, plus 6 + 6 + 6 that I do = 18/35 = 51.4%. Say I get one I want again. 5 + 5 + 6 + 6 I don’t want, and 6 + 6 I do want: 12/34 = 35% of a good outcome. If I get one more I want, then 5 + 5 + 5 + 6 to 6: 6/33 = 18.2%. Any time I get an unwanted puzzle or a duplicate, I have to try again. My chances of getting all four wanted puzzles on just the first 4 tries is very close to 0. This is very similar to the situation where the store clerks restock the machine at night to keep the mix at 6 unique puzzles at all times: 4/6, 3/6, 2/6, 1/6. If the mix is unequal, or some of the puzzles are not in the machine at all, then I’m screwed.

But, as mentioned before, I have 4 puzzles already, and I don’t mind getting both of the remaining 2. The question becomes, how many duplicates are still in the machine, and how many copies of Pyramid and PlainCross? That I don’t know. Essentially, what’s important is setting a limit to how much money I want to spend to find out, and hope I get Pyramid at least, before my money runs out.

Prime Eval, Part 14 – Approximations

Back some weeks ago, I’d made a reference to rectangles as having a possible component that would look like you have a square of side a, and a smaller rectangle attached to it that is a x b, giving you an overall size of”a * a+b”. If you took the area of this rectangle, you’d get a^2 + ab.

This leads into a rather interesting question: What value would you need for a, so that a*a is equal to a+1.
a^2 = a+1
Or, a^2 – a – 1 = 0

The quadratic equation gives:
= (-(-1) +/- sqrt((-1)^2 – 4*(1*(-1))) / 2*1
= (1 +/- sqrt(1 + 4))/2
= (1 +/- sqrt(5)/2

When I was in high school, my math teacher proposed this problem in the form of “what number times itself is equal to that number plus 1?” His purpose in making this a word problem was to teach the concept of iteration. In this process, you start with what you think is close enough. Say, 1.0. Then you plug this value in to both sides:

1^1 = 1
1+1 = 2

Then subtract to get the difference, divide by 2, and add that to the original “a” to get the new value, and repeat until the difference is too small to matter.

(2 – 1)/2 = 0.5
a0 = 1; a1 = a0 + 0.5 = 1.5

1.5^2 = 2.25
1.5 + 1 = 2.5
2.5 – 2.25 = 0.25
a2 = 1.5 + 0.25/2 = 1.625

Pretty quickly, you’ll get to 1.618
However, if you flip the difference operation, so that you use
(1 – 2)/2 = -0.5
a0 = 1; a1 = a0 – 0.5 = 0.5
0.5^2 = 0.25
0.5 + 1 = 1.5
(0.25 – 1.5)/2 = -0.625
Pretty quickly you’ll get to the second answer of -0.618

Which is the same as if you used the quadratic equation. The thing is, I never understood what that “close enough”, or in his words “a reasonable guess” was. To me, it seemed that you already had to know the answer in order to get the answer. Or rather, that you put in enough work on the problem to have a good feel for what the answer should already be, before trying to find it. It turns out, though, that the approximation method works for any value between +/- (1 + 1.618), or +/- 2.618. So, simply picking 0 or 1 is going to get you to the answer within 5 to 6 iterations. Making an excel spreadsheet for this is pretty trivial, but I still like to do it. The answer converges very fast. If you pick a value outside this range, the result goes to infinity just as fast.

This number, 1 : 1.618, is called the Golden Ratio, and a rectangle with this dimension (1 x 1.618) is called a Golden Rectangle. So, for a * (a + b), a=1 and b = 0.618. The Golden Rectangle has been used for centuries in determining magazine dimensions and building design. The ratio shows up in nature, in branch and leaf spacing, and within the Golden Spiral. There are some arguments that the Great Pyramid of Giza is designed based on the Golden Pyramid, with a slope very close to the golden pyramid slope of 51 degrees and 50 seconds.

The really interesting thing is that there’s more than one way to represent the math. One choice is as continuing fractions (which incorporates the Fibonacci numbers):

Or continued square roots:

My favorite has always been the representation as a resistor ladder.

Why mention this? Because I think this kind of math is fun, extremely powerful, and shows up in unexpected places.

Now, Fibonacci. Leonardo Bonacci (c. 1170 – c. 1250) was an amazing guy, and you should read the wiki article on him. The Fibonacci sequence starts either with 0, 1 or 1, 1. To get the next number in the sequence, just add the current two most recent numbers together. I.e. –
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …

This sequence shows up in nature, such as with bee ancestry codes, and seeds on a sunflower. The Fibonacci spiral approximates the Golden Spiral.

It’s all just stuff to think about.

GetaCross 3D Puzzle

It’s kind of funny. I was looking on youtube for different kinds of 3D wood puzzles, and I found one video by American Woodworker on burr puzzles. First, I’ve never heard them called “burr puzzles” (because they look like burr seeds) before. Second, the big 12 piece puzzle is REALLY COOL! Anyway, watching the 12 piece burr being disassembled and reassembled unexpectedly helped me in solving GetaCross.

GetaCross (Geta is the Japanese-style of wooden sandal + cross) is another one of the capsule ball 3D series puzzles. There are 6 pieces, about 4.5 cm x 2 cm, and it’s 200 yen. Because the little slip of papers that come with the puzzles don’t have the solutions printed on them, I went to the main website but couldn’t find this series mentioned there at all. So, I tried googling GetaCross, and all that came back were hits on the phrase “get across”. Not helpful. This made me extra cautious, because if I got it apart and couldn’t get it back together again, I’d have a 200 yen pile of loose pieces, and I could get the same effect just by going to the 100 yen shop and buying some Popsicle sticks. And there have been some puzzles that I never could solve, meaning I have a past history with this kind of experience. So, as I got started, I was almost immediately reminded of the 12-piece burr, and that made things easier in the long run.

Again, the pieces are extremely slippery, making them difficult to hold in place. I did figure out the solution by myself in a few minutes. Actually, I got it right the first time completely by accident. When I tried a second time, I discovered that it is possible to get the pieces wrong and not be able to solve it immediately.

There are 4 identical pieces (they’re different colors, but that’s irrelevant), one that has a slightly longer tab on one end, and one piece that has a notch in one of the long sides. This should tell you how to put the thing together right there.

Take three of the identical pieces and hold them in place as shown in the photo.

Take the piece with the longer tab and put it into the gap at the top of the assembly, with the tabs facing down, and the longer tab on the right hand side.

Push the top and bottom pieces to the left about half an inch to an inch and angle them so that the remaining identical piece can be fitted into the notches on the left land side.

Carefully reposition the existing pieces in the assembly so that they’re in their respective notches, and they’re either lying flat or standing perpendicular as the case may be. (Basically, straighten everything out so the pieces fit together correctly.)

Slide the top piece to the left one inch, or at least enough so that the piece with the notch can fit into place on the right hand side. Position the notch to be on the top of the piece.

Then slide the top piece all the way to the right until it stops moving. You’re done. Not a terribly difficult puzzle, but a frustrating one because the pieces keep sliding and falling apart. I should take sand paper and roughen up the inner surfaces a lot, I guess…

To take it apart, just find the one piece that slides out, and slide it out until it clears the piece with the notch. Let go and it’ll disassemble under its own weight.

Prime Eval, Part 13 – Light

After reading Richard Feyman’s book, QED, I got to thinking about the recent spate of astronomy articles on Specifically the ones about finding ever more distant, older galaxies. According to the Feynman diagram, electrons randomly emit and absorb photons, and photons are particles that act like waves. So, here you have this galaxy, which has millions of stars, and each star has an uncountable number of electrons that are firing off photons all over the place. And some of those photons are aimed in the direction that Earth is going to be in 16 billion years.

And now, for 16 BILLION years, those poor little photons are zipping along, waiting to intercept another electron in order to move on to the next phase of emit and absorb. Naturally, some of those photons will run into cosmic dust, or other high velocity particles, along the way and be re-radiated, but there will be 16 billion year old photos that were never absorbed. And, if Feynman is right and photons are particles, these are 16 BILLION years’ old particles. If they had decayed, they’d have to reconstruct themselves again right away, and keep doing that along the entire trip.

One of the side corollaries of Einstein’s E=mc^2 formula is that as an object approaches light speed it gains mass (according to my physics professor in 1982; who knows, maybe the definition of mass has changed since then). And what travels at light speed? – Light! But, if light is made up of photons, and photons are particles that act like waves (as Feynman said), and those particles have mass, why don’t photons have infinite mass when traveling at light speeds? Additionally, if you slowed them down to less than light speeds, would the mass of photon particles go to 0?

There have been a few videos on youtube purporting to show what our solar system would look like to a ship traveling at light speed. A few commenters have complained that the math used in these simulations is for out-of-date formulas for General Relativity. Me? I’m wondering what the universe would look like to that 16 billion-year-old photon…

Which brings me to instantaneous travel. The thing about light is that it isn’t instantaneous. It may look that way at short distances, but as we know, light takes time to go from point A to point B. In fact, the speed of light is close to 3.00×10^8 m/s. The reason this is important is that by knowing how long something is going to travel, you know where it’s going to stop. That is, if you get into a car in Chicago, and drive around 8 hours in a northwesterly direction, when you stop you’ll be in (or right around) Minneapolis. Draw a line from Chicago and Minneapolis, specify a velocity for the car, and you’ll easily be able to determine where along that line the car will be if you stop it at time “t”.

But, if you invoke instantaneous faster-than-light transportation, the time taken from point A to point B is going to be 0 (or to any other point along your line). And if it’s zero, you’ll have no way of controlling where you are along that directional line. In fact, you will be on every point of that line simultaneously, and when you stop, you could end up anywhere (or, you turn into an infinitely thin plasma and end up nowhere at all).

So, if you look at Star Trek-style transporters, they can’t be instantaneous, because you wouldn’t be able to control where you reappear. And if they are near light-speed, you’re creating what is effectively a death ray (both for what you’re teleporting and what you’re aiming the teleporter at). I still argue that it’s better to melt down your passengers at point A, and just transmit the recipe for recreating them with a 3D printer at point B…

3D Diamond Puzzle

Diamond is from the same capsule ball collection as Galaxy. It’s much easier to take apart and put back together, and it’s also 5 cm side to side. 200 yen. On a scale of 1 to 5, this is about a 0.5.

Diamond is almost exactly like Soccer Ball except for 3 differences. 1) It’s cubic instead of spherical (not a major issue). 2) All 6 pieces are identical. 3) Because they’re identical, there’s no dedicated locking piece. It’s this last point that makes assembling Diamond slightly different from Soccer Ball. They start out the same, though. Just follow the instructions for Soccer Ball all the way up to the last step.

The pieces fit together fairly loosely, so slide the last one into place and let all the others push apart relatively freely without completely disassembling. Then, as the last piece slips into place over the others, push them together to get the puzzle to self-lock.

Unfortunately, because it is self-locking, if you put the puzzle on its corners instead of sitting flat, it will disassemble under its own weight. Not a very good design, and probably the worst puzzle in the series.

Two Birds kiri-e

My sister suggested that I make a kiri-e for my parent’s wedding anniversary. To find a suitable pattern I went to Junkudo bookstore and checked all of their books on kiri-e, but mostly they were for kid’s patterns, or gothic lace. I’d mentioned back in October that I’d found one book called Utsukushi Kiri-e, and it had one pattern I liked. It took me about 3 solid days to cut the border and then glue in the colored construction paper. This is probably the most detailed thing I’ve made so far. Finished size is a sheet of A4 paper (8″x12″). I think it turned out ok.

Prime Eval, Part 12 – Force Fields

There was an article on, which I can no longer find, that proclaimed that researchers were close to “Star Trek-level” force fields. The article talked about the use of ultrasonic waves to create “force pockets” that allow the operators to move small objects, levitate them, and manipulate them in limited ways. After reading the article, I really wanted to write up a blog entry on how writers don’t understand the concept of a “field” from an electronics, or physics viewpoint. More specifically, I wanted to rant about how the “field” only worked horizontally – you wouldn’t be able to make a vertical field.

Direct youtube link 1

But then, when I went to youtube, I discovered the work of some researchers at the University of Tokyo in 2014, showing some very sophisticated levitating manipulation. This was followed by a second video presented at SIGGRAPH in the same year, proposing ultrasonic projectors for vertical 3D graphics. The process involves matched transducers that create standing acoustic waves that can trap small, light objects. I don’t really consider these to be “fields” in the standard science fiction sense, and they’d fail completely if applied as shown in Star Trek as a protective ship barrier, since there’s no air in deep space. Still, the concept is really cool, and it makes for some fascinating software applications. (They really should have demonstrations of these transducers at SF conventions, if they don’t already.)

Direct youtube link 2

The stupid part is that the youtube commenters keep asking if this is how the Egyptians built the pyramids. (Short answer – “no, it isn’t”.)

3D Galaxy Puzzle

I was surprised recently to find that one of the capsule ball machines in the Tenmonkan shopping complex currently has a line of 6 small 3D puzzles for 200 yen (approx. $1.80 USD) each. I decided to take a chance on one, and received what the company is calling “Galaxy”. Doing a yahoo search, I found a larger, more complex version under the name “Meteor Star”, and this same version on youtube (with video instructions) as “Falling Star”.

There are a few differences between Galaxy and Falling Star that make the Japanese version harder to solve. First is that Galaxy is only about 1.5″ long corner to corner, and the surfaces are very slick.

So the pieces are harder to hold on to and keep slipping around and falling on the floor.

Second is that Falling Star has two longer pieces with square notches in the middle, and one longer piece with a half-notch. The half-notch piece fits snugly into place on one of the full notch pieces, creating a stable starting point for assembling everything else. Galaxy, though, only has 3 full-notch pieces (5 smaller notched pieces, and the locking pin piece). The assembly is the same, but again, the pieces slide around too much – you really need to have two sets of hands on this puzzle.

The trick is to put one of the shorter pieces on the longer piece first as kind of a stabilizer. Afterward, the assembly is just like in the youtube video. I admit that I needed to resort to the video a lot because the capsule toy didn’t come with instructions. I knew how to unlock the locking piece at the beginning, so taking it apart was fairly easy (unlocking is a bit challenging though, just because it feels like you’re going to break the puzzle). And I got really close to getting it back together again, except that I couldn’t figure out how to orient the third long piece to put it in right. Once I got that, finishing the kit became trivial. Again, though, locking the last piece in place takes a fair amount of force, and because the kit is so small, there’s this sense that the piece is going to snap in two. I can disassemble and reassemble this kit in under 40 seconds.

(Take the second longer piece and put it on top of the short bracing piece, with the wide notch facing up, and the short notch facing the first piece.)

When I got ready to take photos for this blog, the locking piece was so hard to turn that I had to use my penknife to crowbar it. In the end, I shaved the locking piece axle pin to thin it a bit and round the inner corner off. With this mod, it’s a LOT easier to turn and lock, without actually unlocking on its own.

(Take the remaining long piece and orient it so the long notch is facing up and the short notch is facing left. When you pick it up with your free hand, turn it 90 degrees counter-clockwise so the short notch is facing down.)

Because the puzzles are so small, and only 200 yen each, I’m willing to try my luck on the capsule dispenser to see if I can get 2 or 3 of the more interesting ones. I’m thinking that I’ll spread things out so that I only buy one capsule ball a day. Hopefully, I’ll get the ones I want before the machine is changed to dispense something else. (There was one machine in the Amuplaza department store that had Japanese ghost fox keychains for 200 yen that I was somewhat interested in, but apparently I waited too long because I can’t find it in Kagoshima any more.)

(Put the remaining long piece against the side of the first one, in the little exposed notch. This is where things start getting tricky because the pieces keep slipping. This is also the step I kept getting wrong.)

(Put one of the short pieces in the long notch on the back of the long arm you just put on. This stabilizes the puzzle a little and gives you something to brace with using your work hand. The pieces face each other to make a flat assembly.)

(Put the locking pin piece into the upper notch. When it locks, the axle pin part will be at the top right corner (as referenced in this photo). But, as you’re assembling the puzzle, you want the axle pin part rotated to be at the lower right corner, as shown in the photo. Follow this with another short piece. Put it in the front part of the notch (nearest you) of the long arm you just put on. This should strengthen the puzzle enough now that it doesn’t fall apart so easily.)

(Lift the locking pin piece to create gaps beneath it, and slide the remaining two shorter pieces into place on both sides of the arm.)

(All of the pieces are in place now, and the locking piece is shown still in the raised position. Note that the axle pin part is facing you, and is rotated so that the locking piece can move up and down inside the notch.)

(All that remains is to rotate the locking pin so that the axle pin piece is at the top, facing you. This step may require a certain amount of force, but it shouldn’t be hurting your fingers. If the rotation is really difficult, disassemble the puzzle, shave the inside edges of the axle pin a little bit, and try again.)

How to solve the Falling Star puzzle (AKA: Galaxy)
direct youtube link


Prime Eval, Part 11 – Knowledge Rant

I apologize. I’m going to rant on something. It’s peripherally technology-related, so I’m going to claim it belongs here.

Some time ago, I was reading Brian Anderson’s Dog Eat Doug strip, where Brian has his main character, Sophie, make a reference to a joke Joe Rogan made about cats. Joe played Joe Garrelli on Newsradio, hosted Fear Factor, and is currently a commentator on Ultimate Fighting Championship. One of the commenters at GoComics wrote “I have no idea who Joe Rogan is, or why he has a “take on cats”…”

This confuses me. This person is reading a comic strip on their computer. They are literally right in front of their computer, using their web browser to look at a web page. It takes less effort to type “joe rogan” or “joe rogan cats” into google than it does to type out that comment. If they’d used google search, they’d have gotten the answer to both “who is joe rogan” AND “what is his take on cats”. On top of this, they’d get the joke, while AT THE SAME TIME preventing themselves from looking like sluggish leeches. Because, they’re not only expecting someone else to do the search for them, but that that person is going to spend several minutes typing the answer to spoonfeed them.

But no. Here we have individual machines in our hands with more power than anything anyone in the world had in the 1970’s, connected to a search engine that can find matches on billions of webpages within one to two seconds, and that can pull up links to wikipedia pages that often have dozens of articles summarized and stitched together in just one place for simple access. I mean, we have all this information and the power to find what we want within all that, and people still want someone else to hand the answers to them.

Think about this. We have the option of learning almost anything we want – how to perform brain surgery, speak multiple languages, design space stations, or peal onions with just a vacuum cleaner, and we don’t want to make the effort. This person couldn’t be bothered to figure out the punchline to a joke because… it would eat into the time they were spending reading comic strips? Now, I realize how petty this sounds, and that I may be overreacting here. On the other hand, I see the same kind of behavior playing out on Facebook, youtube, Twitter, you name it. The above example is not just an isolated incident, it’s standard operating procedure for people. I do understand, though, that not everything is worth learning about. There are lots of times when I see something in an article or a reference to something that I’m unfamiliar with, and I just skip past it because I don’t care. But, that’s different from people that proudly announce in front of an audience, “I don’t understand the joke and I’m too lazy to look it up.”

Mankind as a whole is standing on the cusp of a new age in self-education. The question is whether we’re willing to expand our awareness of the universe around us by ourselves (and with the help of everyone writing this information on the net), or if we’re not. Which leads me to TSOJ’s law: “We are only as educated as we allow ourselves to be.”
Corollary: “Most people have no allowances.”

Dinosaur Egg 3D Puzzle

When I was looking at this puzzle in Thailand, I loved the design and was thinking that it would be really challenging to reassemble. But, when I actually sat down with it in the hotel, I realized immediately that it’s just a variation on the Soccer Ball, and is just as simple to do. They’re pretty much the same puzzle, while Egg just has 2 more pieces, and the 2 spines are a little longer than the other notched pieces. If you can do one puzzle, you can do the other. Again, I can take this one apart and put it together again in less than a minute.

I found this puzzle, and Soccer Ball on the Brilliant Puzzles website. A comment on Brilliant Puzzles. I was looking over the descriptions of the two Thai puzzles on the BP site, and I noticed quite a few spelling and grammar errors. Most of the mistakes seemed to be Asian in style, so I was thinking that the site might have been designed and hosted in India or China. But, according to the “Contact Us” page, they’re based in Georgia, USA. Kind of embarrassing to see these kinds of spelling errors coming out of the U.S.

Sort the pieces. There will be 2 longer “spines”, 2 pieces with two notches, 4 with three notches, and the locking piece.

Take one of the spines.

Put one of the two-notch pieces into the lower notch of the spine as shown.

Put the other two-notch piece into the upper notch of the spine.

Put the second spine over the 2 two-notch pieces to hold them in place.

Take one of the three-notch pieces and mount it into the right side notch of the bottom piece. Orient it so that the edge that has one notch is pointing up, and the edge with the two notches is facing against the spines.

Do the same thing on the other side of the bottom piece.

Put the remaining three-notch pieces into place in the notches of the top piece. This may be a bit tricky since they’re going to want to fall out due to gravity. You should have a diamond-shaped hole in the middle of the egg if you did this right.

Then, slide the locking piece into place and you’re done. Note that the ends of the locking piece are curved one way, and straight the other. You want the ends rotated so that the curves match the curves of the egg left-right, and are straight top-bottom (unlike in the above photo). If the locking piece doesn’t slide into place smoothly, resettle the rest of the puzzle assembly to make the diamond-shaped hole a little bigger and try again.