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In summary, Rite Aid offers a wide range of puzzles for all ages and skill levels, including jigsaw puzzles. Donating used puzzles to charities, selling them to make money, or extending the life of pre-loved puzzles can be a rewarding experience.
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📹 Why don’t Jigsaw Puzzles have the correct number of pieces?
CORRECTIONS – At 22:31 I say “214” but the correct number on the screen is “2014”. First spotted by coolpeepsunite who really …
One aspect you have missed there. There seems to be a preferred non square piece ratio some puzzles tend towards. Especially Gradient and solid color puzzles do so in order to be a bit easier (2 possible orientations instead of 4). Also piece interchangability has to be minimized and making the pieces non square reduces the problem by at least half.
There’s one caveat to this that I’m surprised you didn’t consider – puzzles aren’t necessarily grids. Whilst the top might have 50 and the left side have 20 for example, there’s no guarantee or requirement that every column and row has that same number. So a puzzle maker could also fudge the numbers this way to get the exact piece count. I’ve come across many jigsaws that don’t conform to a grid structure (they are definitely harder)
I think one thing you’re missing about the fundamentals of jigsaw puzzling, is that a lot of people don’t really want perfectly square pieces. That Monopoly puzzle with a piece ratio of 1.6 had some beautiful pieces in there! My most favorite puzzles are the ones with relatively high piece ratios. They actually have terms for this. There are Ribbon Cut puzzles, which purposefully have lower piece ratios, and Random Cut puzzles, which purposefully have high piece ratios. When looking for my next puzzle, I go out of my way to buy random cut, because I love a variety of different piece types. Still relatively square or rectangular in shape, not the wild ones where almost every piece is its own type, but where there’s a collection of 5 or so unique piece types. This test you did doesn’t really work unless you specifically go for ribbon cut puzzles.
I think the squareness of the puzzle piece contributes to difficulty. Perfectly square pieces can’t be reliably placed on their x or y axis because the deformity offers that sort of clue. Unless the cardboard or paper had a grain you could detect, perfectly square pieces could go in 4 orientations, where a clearly rectangular piece has 2. This might explain why the Monopoly puzzle, probably marketed to a less skilled puzzler, has such rectangular pieces when square would have been just fine.
Side note on the gradient puzzle: While yes, you don’t need to be constrained by picture size with it. Most manufacturers don’t actually make a new cutout for every puzzle and instead reuse the puzzle pattern multiple times while changing just the image. So the 2000 pieces puzzle is like that because of all the other puzzles that use the same template. Also side side note: Tim Klein is an artist known for getting a bunch of puzzles with the same cutout pattern and splicing them together to come up with a original looking amalgamation.
The piece count for 1000 piece jigsaws has changed over the years with the move to widescreen TV. When people were used to 4:3 screens, jigsaws used to match that ratio, and the best match for 1000 was 36 x 28 which gave 1008 pieces. Now that we’ve all gone widescreen, it’s much more common to get 40 x 25 which gives exactly 1000 pieces.
Fun fact. Extra pieces don’t cost the manufacturer anything. Any regular shaped puzzle of a given size will have the same area (and therefore the same material costs) regardless of how many pieces it is cut into. The only cost related option is the number of ‘blades’ on a cutter which will increase/decrease the piece count by a whole row or column at a time. Even non-grid cuts will use the same area and so the only cost increase, for say a laser cut puzzle, would be the extra time (and energy) to cut the extra pieces.
I kinda find it hilarious that Matt, despite not deserving it, has become a pillar for math mistakes the world over. Parker Square, and now Parker Counting. That he takes it in stride I think is a lesson worth learning: we all make mistakes, despite this, we are all capable of acknowledging, understanding, and growing from them. So despite Matt’s position as this mistake maker, he has also become a good example of what making mistakes should feel like: goofy, maybe a bit embarrassing, but nothing to beat yourself up or lose hope over.
I checked out my collection of Ravensburger to check and I have two things to say: 1. Actually Ravensburger writes not only the dimensions but also the piece count on the side of the box, just not the front or back 2. The piece counts for my collection are: 3 of my ‘1000’ pieces actually have 1008 pieces 1 ‘1000’ piece puzzle actually has 1000 pieces 1 ‘1500’ piece puzzle has 1530 pieces
I created a puzzle game (Jigsaw Puzzle Dreams) and you can type in the size of the puzzle you want. Recently saw a streamer that was trying silly puzzle sizes like 1 or 2 pieces and the game adds in a few more pieces to keep correct aspect ratio. Streamer and chat kept going on about how the developer needs to learn how to count!
It seems to me that the loss function for each additional piece over the advertised value should actually be calculated as a percentage over. In the extreme, say you had a puzzle with a billion pieces! Well, 1,000,000,001 pieces isn’t far off at all. But if the puzzle was only 15 pieces, 16 pieces would just be absurd!
Now that you’re almost at a million, I can say this without feeling slightly bad about it: when I first heard about you, I thought that “stand up maths” was perhaps the absolute most niche youtube website concept I could possibly think of. I thought “well gee, that is the least commercially viable idea I have heard in my entire life!” I have never been so happy to be so wrong. Sometimes I feel like an absolute weirdo; an alien living in a human’s world, trying to figure out how to fit in. But then I see that some dude made a career out of the seemingly insane concept of fusing mathematics and humor…. and it gives me a little hope. Not only does that tell me that there are other weirdos out there who also like weird things, but that maybe, just maybe… things will turn out ok for me too. Anyway, thanks Matt, and cheers to your continued success 🙂
A tip for counting things like puzzle pieces or pennies by hand. If you use 3 fingers, one per piece you can count three at a time and do 3 rows of 3 with one on top for 10. Or, you can do four fingers for two rows and two fingers to grab the 9th and 10th. Makes it go faster and visually a 3×3 + 1 stack is easy to visually confirm.
I must say I was just the slightest bit disappointed you didn’t work out a badness rating based on real-life examples beforehand. A comprehensive study of ratios in existing jigsaw puzzles just to teach a computer program to predict the actual number of pieces in a given jigsaw puzzle would have been a perfect fit for this website! 🙂
More interesting than just making up the “badness” would be to figure out how the company determines “badness”. Look at every puzzle, see the possible layouts, and see which they picked. Do that for enough puzzles, and you can see exactly how far “off” they’re willing to go, and what they’d rather sacrifice. That would be an interesting Machine Learning problem, where you’re essentially making the “minimal” badness being the puzzle the company chose!
I’m surprised you didn’t mention alternative piece shapes in this article and how that might play into these calculations. In my experience, many puzzles don’t have exclusively rectangular pieces. Sometimes they have a regular grid like the ones you describe but with some pieces essentially being split into 2 triangles instead of 1 rectangle in various places and some having no overall grid-like pattern due to the sheer variety in piece shapes. Though I don’t really blame you for omitting this since I imagine that it would be extremely difficult to account for those factors in a computer program like jig.
As someone who’s been puzzling for many years, I’ve never counted the actual number of pieces nor have I cared, lol. My biggest pet peeve with puzzles is quality. I.e. Are the pieces cut properly, do they hold up over time & not peel away on the tops or bottoms? My family passes around a lot of puzzles, and in my opinion Ravensburger is pretty solid & their puzzles withstand the test of time.
To make this interesting, I’d love to see how trends change over time. As someone who has done puzzles for close to 40 years here’s what I’ve noticed: Picture ratio: The desire to stay close to the golden ratio has gone down by an extreme amount. Square puzzles are not a new thing, but they are far more common now. “Panorama” style are definitely new, they certainly didn’t exist before. The one style that has gone down in popularity (probably justifiably) is portrait-style puzzles where the ratio is close to the golden ratio. Grid ratio: The desire to have a nice even number has gone up substantially. I’d say that 60 – 75% of the puzzles I do today do match the number on the box. When I was a kid, it was around 5-10% Piece ratio: The desire to keep this close to 1 has gone down tremendously. I’ve seen so many more puzzles with squashed pieces (like your Monopoly puzzle) now. I don’t know if it is to show that they can, or what. In general, quality has gone up with time, so this could be the reason. With the cheaply made pieces of the past, squashed pieces would frequently break in the middle, but with better quality control, that is rarely an issue today. I have a lot of the 1000 piece puzzles I did as a kid, and they were all landscape style golden ratio puzzles all but one had exactly 1008 pieces (28×36). The one exception was 25×40, which has honestly become the norm today.
Some thoughts I had regarding puzzles: – I’ve been doing some 1000 piece puzzles by Buffalo Games recently, and they’re actually 27×38 pieces, meaning they actually have 1026 pieces. – There are some puzzles that use a “random cut” rather than a “ribbon cut”. A ribbon cut is what your see here when all the pieces make a nice grid and you can just count the sides and multiply. With random cut, you have a wide variety of piece sizes and shapes, that don’t make any discernible pattern, so you can’t just count the sides and multiply, you’d actually just have to count all the pieces.
I thought Matt was just gonna put the frame together and do the math. The moment he started manually counting, I just knew that either he’d miscount, or he’d lose a piece somewhere, leaving whomever decides to assemble it that unsatisfying feeling of an empty spot… Sidenote, I didn’t know it was all that desirable for the pieces to be as close to a square as possible. Most of my jigsaw-ing I did as a child, but I remember a ‘standard’ puzzle piece being closer to 1:4⁄3
You might want to add a picture analysation to JIG, as there seems to be a correlation between “little contrast and structures in wider ares of the picture” and “piece Ratio further from 1”. explanation: clearly “off” piece ratio makes it easier to solve because to rotation options reduce from 4 to 2. This is acceptable for puzzle freaks, when it`s still hard for other reasons.
Hey Matt! Had a math debate with my family that relates to puzzles! As you double the amount of pieces in a puzzle, does it take a proportional amount of time to do the puzzle, or perhaps exponential or quadratic? I think it is exponential because for every new piece you add it makes every piece before that take slightly longer. Would love to hear what you think
Hah, I had the same problem in my bachelor’s thesis. I had to quantize an N-Dim space with some sample points. The grid had to be as isotropic as possible while the total number of sample points needed to be as close to a power of two as possible. The method/formula later also appeared in a paper, in case someone is interested i can link it :).
I remember perusal this guy live as part of a school excursion at around 6 years ago and was hooked into maths. I distinctly remember him looking at LCD screens through a microscope to seeing the individual red, green, blue pixels, as well as his pi scarf. So cool to see him with over 1M subscribers.
“why be constrained by the size of an image when it’s just a gradient” – because they’re not constrainted by the image, the image is constrained by the jigsaw templates they cut them with! I bet you that the vast majority of puzzles of the same number of pieces and sizes can have the pieces inter-changed and still fit together perfectly!
So something that you aren’t accounting for in the “too many pieces” idea, for the manufacturer once the die has been made to cut out the puzzles of a given size, it literally doesn’t cost them any more to make a 1000 piece puzzle than it does a 2000 piece puzzle because they literally just print the image and then cut it with a die (sometimes they will perforate it with a die before printing but that is rarer) Also if you get 2 puzzles from the same manufacturer which are the same size and dimension, all of the pieces will be interchangeable between the 2 (Assuming they are both from the same life cycle of the die) because they will use the same die for every puzzle in a particular line
17:30 – As a child, I used to love the swings and the slide, the roundabout and the strange horse thing. I loved it so much, that I went there every day, until all of the attendants knew me by name. Now, obviously, this was free, but they said that if there had been a charge, I would probably deserve a ‘Frequent Member’ discount. There: That’s my Park Account Joke.
Interesting, going down the comments i expected someone to speak out about the betterhelp sponsorship. Looks like this audience isn’t aware of how controversial the reputation the company has, after it was revealed some years ago that they weren’t properly vetting the credentials of their therapists. I’m surprised they haven’t rebranded to try to restart with a clean reputation.
It would have been amazing if someone trolled Matt when he was making this article by giving him the 200 piece puzzle at the start with 4 of the pieces missing, knowing that he was going to be filming himself when he discovered that the puzzle of him claiming that the puzzle that claimed to have 200 pieces had 204 pieces had 200 pieces after all.
1:30 My brain kinda broke when I realized the strong image-inception going on…How did he take the photo for the puzzle of him sitting there, with the puzzle already solved in front of him… which was there first? Is it a lie? An edited photo for the puzzle? Will we ever know? How many Matts are even there in this frame? And how deep do we have to dig until the repetition stops….
I now wanna know if the 1000 piece circle puzzle I have is actually a 1000 pieces, but I don’t wanna count them manually so my brain is trying to figure out if there is a better way. I can’t just count the sides because circle. I might be able to get the picture and the piece ratio but the pieces are quite diverse in shape so not sure if that will work out. I could count by circle and hope there is logic in with how many pieces it increases each time, but I don’t think the amount it goes up with each circle will be constant. I might just be stuck with counting manually but if anyone has any suggestions on counting circle puzzles feel free to trow them my way.
I love the “worlds collide” feeling when one of “my” creators crosses paths with another of “my” creators. If I were creating puzzles, I’d be tempted to make 3-4 double pieces & a some half pieces. A way to adjust the piece count while maintaining the picture & grid ratio, except for those oddly shaped pieces.
This is really funny, just 4 days ago I reopened a “1000” piece puzzle, and wanted to check all of the pieces are still there, because finding out too late would be the worst. spoiler alert, we ended up counting more than 1000 pieces, and I realized it might have more than a 1000, and it took us like 1.5 hours to spot the mistake lol. To be fair, all of the pieces looked identical so I hadn’t even considered a non-square ratio. Long story short, we counted 1007 pieces and I guess that’s 2 hours down the drain /: at least didn’t feature it out half way in though
I’d call the piece count on the box a “nominal size”, i.e., an approximate value close to the actual size and convenient for marketing. Likely most folks don’t really care about the exact piece count. This is similar to construction lumber. The 2″ x 4″ board and other sizes have not been that actual size for many years, if ever, but still carries that name. The nominal sizes typically were the sizes of the rough cut lumber, before drying and planing. A few years ago there were two lawsuits in Chicago over the nominal lumber size vs actual size. Both were struck down. Should puzzle manufacturers be sued over this similar issue? No, it would be a big waste of resources. What about the piece count in round puzzles? I have done some recently that have a wide variety piece shapes and sizes. No completely consistent piece size ratio.
I learn this a few months ago. I bought this used wooden jigsaw puzzle quite cheap and diceto to count the pieces (250p said in the box) and it was right 250 inside (In my mind was glad it was complete) then when I finish the puzzle I had one extra piece (not a copy from another piece, just a piece with a random image not related to the puzzle haha). I did counted again just to make sure and the puzzle actually had 249pieces it make sense they would add one more to sell it like a 250 pieces 😅
presumably the biggest factor for the people actually making these decisions is how it affects the manufacturing process. So rather than caring about “squareness” they care about “how small of a space between cut lines do we need” or “how finely does the cutter need to move to navigate this”. And rather than caring about having extra pieces (same amount of material is used regardless of how many pieces it is cut into) they care about the total number of lines that needed to be cut.
There actually is “an ultimate best way of doing this” and that is to have the pieces be as close to squares and there’s a good reason for it. If you could easily see if a dimension of a piece is larger than the other dimension then that effectively halves the amount of placement orientations and makes the puzzle much much easier to solve.
I remember solving a 1000pc jigsaw puzzle years ago, and yes it didn’t have any extra pieces and the picture is 40×25, which is 8:5 ratio. Another one was a 500pc which results into a 25×20 picture, and a 5:4 ratio. If ever I tackle a true 200pc puzzle, a better fit is a 2:1 ratio having 20×10 pieces. As it turns out that last one will not fly. Maybe 300 pieces could be good…
Before perusal (@10:13), the 1000 piece puzzle will be 36 x 28. That would be 1008 pieces with a grid ratio of 1.2857; which is 0.0754 off 1.3611. I was wrong on that puzzle, but a later “1000 piece” puzzle DID have 1008! 🎉 Disney puzzle will be… 43×35. 1505. (Guess @20:37) I got Jig’s guess! But we were wrong. 😑
I think one thing to consider too, is that the pieces aren’t individually created. They’re cut from a single sort of “proto-puzzle” of the image printed onto whatever cardboard/cardstock/wood they’re using. The additional cost in having extra pieces doesn’t have anything to do with the material of the pieces, but rather the material/energy (if it’s laser-cut wood, for example) of the cutter, which gets smaller the more puzzles you make with that configuration. Trying to get as close as possible to the advertised number is pretty much entirely a human psychology/truth-in-advertising thing, not anything to do with manufacturing extra pieces.
So…. If I were to expand on this (and I won’t because I don’t have enough time and/or jigsaw puzzles) my next step would be to separate puzzles by manufacturer and see if you can hone the algorithm by adjusting the weights until it accurately predicts per manufacturer. It may turn out that each manufacturer has different preference thresholds for square pieces vs. correct counts.
Interesting. But I have hundreds of puzzles and, geeky as it may be, I put them all in a spreadsheet (you’d love it!) That shows the grids and ratios. Plus number of pieces and it turns out there are quite a few with fewer pieces than declared on the box! (Edit: it’s never bothered me, whatever Karen may say. And almost all my 1000 piece jigsaws (dozens) are 40×25 often with odd aspect ratios if I may use the term)
19:00 – I’m a little disappointed that, after knowing it was a square, you didn’t put the height and width in as 1, 1. You said it was a ratio calculation and units don’t matter, so almost feels redundant putting in the same number twice. I guess for the content. Missed out on some cool points though.
I’ve wondered this, myself! I’ve noticed the edges are X × Y, which answer is often not the number that matches the promised number on the box. It’s bugged me for a long time, actually! 😄 I remember when I was little, doing a (If I recall correctly – it was about 5 decades ago) 50 piece puzzle (it was definitely a small puzzle, but not one of those little baby puzzles, either), and was mad that the number of pieces I counted didn’t match the number on the box! I remember it making such an impression on me! So… thanks for doing this!
I would guess there is a limit to piece ratio depending on piece size, because if the ratio gets too extreme one side of the piece might get too small to make a good jig there. And the manufacturers probably use some kind of fidelity measures they tested out on puzzle enthusiasts to come up with their own weightings for “badness” as your python bot has them.
The pieces shouldn’t be squares as stated at 7:24. They should be shapes that have the same size ratio as the image, as in, smaller versions of the whole puzzle. So the piece ratio is how far off the dimensions of the piece are compared to the picture ratio. It should only be a square when the picture is a square, like the Monopoly puzzle.
4 days ago I bought a puzzle and target. When I went to open it at home I noticed the box seemed to be sealed with hot glue and the pieces didn’t come inside a secure plastic bag. My initial thought was, ‘oh no, did someone buy this and reseal the box so they could return it for a refund’ First thing I did was count the pieces individually while sorting the edges. Sure enough 1026. I finished that puzzle today and a few hours later this article was recommended 🤔
This is a throwback to the classic question of whether or not a bicycle has one wheel. I remain in the camp who says yes: just because you exceed the stated quantity doesn’t mean that the statement is false. Therefore, a box that says 200 pieces is accurate if the box includes 204 pieces. There are definitely 200 pieces in that box
I have a “1000” piece puzzle I started a few years ago, but gave up on. Found the box with the remaining pieces and the mat with the solved stuff recently. It’s a Tube Map, so it has so much white on it, hence why I gave up. I also have one that’s a “100” piece jigsaw I bought in a charity shop. It was a Rubik’s Cube themed one and said on the box that one piece was missing, due to it having one piece that could be in two positions. I counted the pieces and it had 99. I took it to work at a school and got some kids to do it to keep them quiet. It worked and they did do it, but it turned out that the trick with the one piece that could go in two places was included as part of there being 100 pieces (so it technically needed 101 to solve it) and it just happened that the person who donated it to the charity shop hadn’t included one of the pieces, so in essence it had two missing when the whole point was that it had one missing. Made it even funnier that I got some kids to test it out (I had those same kids do some coin flipping for some statistics coursework too, I learned from a Maths teacher that getting kids to do the tedious stuff makes things fly by).
Fun puzzle fact, among the common small numbers of pieces, the turnover point where the number of interior pieces (area – perimeter) outpaces the edge pieces (perimeter) is 48 (6×8 grid), which has 24 of each type. My kid got super into puzzles and I wanted to know how many pieces a puzzle needed to have before teaching him the edges-first strategy (which I only consider valuable because there are fewer edges and they’re easy to recognize). We have a few 48-piece puzzles and he’s learning what an edge is. Looking for the next piece count higher now. 🙂
I admit that in all my years of puzzling, I have never paid close attention to the actual number of pieces. I’ve never bothered to count and confirm or deny if the number on the box matches reality or not. What I have paid attention to is the outer dimensions- to make sure I have an adequate table area to start on. And I have found that those are not always accurate! It may claim to be 14 inches by 11 inches, but might actually be 14.25 inches by 10.875 inches, or something like that. People prefer nice, “round” numbers. A “200 piece puzzle” is easy to comprehend. A “204 piece puzzle” would throw some people off. “14×11” is easy to understand. “14 ¼ x10 ⅞ ” sounds too complicated. Of course, some kooky puzzles are round, or some other shape; some have random weird shaped pieces. I had one that used an M.C.Escher tesselated lizard shape, and no defined edge: so all the pieces were the exact same shape, you had to go by the image. Technically, there is no one “right” way to create a jigsaw puzzle. It does not have to be in a grid at all; the pieces do not have to be square(ish) at all. But that is the average, customary way to do it. Rectangular shape, sides straight, approximately square-shaped pieces with sticky-outie bits and sticky-innie bits, arranged in a grid across and down.
If you’re reading this, please reconsider working with Better Help in the future. They have a bad track record of hiring unqualified people and just generally not living up to the ethics you’d expect of a therapy organization. I get sponsorship is important on YouTube and at a glance they seem like a great organization to work with, because they theoretically make therapy more accessible. But it really is a shady company, sadly.
Would have loved to see a more refined algorithm for choosing the correct option. Obviously it was subjective in the end and probably a coin flip from the manufacturers, but I think you were on the track to something really cool! After gathering your results, you could have adjusted the badness percentages until there was an optimal equation for guessing the observed values.
I had a puzzle some years ago with pieces based on triangles rather than squares. An interesting innovation; though aside from that, it was a regular jigsaw puzzle, basically lots of little bits assembling to make a rather pedestrian picture. I’ve always wished jigsaw puzzles came with a couple of spare pieces, to replace the ones which go astray. Much like hardware incarnations of PAR files.
I’m at 10:55 and noticed that you’re measuring the wrong dimension. The box should illustrate a photo of the jigsaw. You should be measuring the dimensions of the white border, not the black border (ie the photo of the completed puzzle and not the box). The fact that the actual Jigsaw has a black border, is false advertising.
So much fun! I think Jig should adjust its extra piece “badness” to be even lower. Puzzle manufacturers don’t “put extra pieces in”. They start with an uncut image of certain dimensions, then decide how small the average piece is going to be, which is a matter of programming the cutter differently, as opposed to throwing in a handful from the “extra pieces” bin. This means the only “badness” in terms of number of pieces is how the puzzle builder feels about having extra pieces, rather than it being an extra cost to the manufacturer. So how bad do they feel? Considering every puzzle builder has to interact with the piece ratio for hours, while few of them likely bother to count the number of pieces, I imagine that having an ugly piece ratio is far worse for the builder than having a bunch of extra pieces. On a separate note, this got me thinking that the size of the piece ratio is likely a strong predictor of a puzzle having the exact number of pieces it says on the box
Fun fact: They don’t care how many pieces there are aside from being very close to advertised. There’s essentially no extra cost since they make the picture whole and then use a big cutting press to cut the puzzle. Even funner fact: LARGE puzzles (I’m talking the 8,000-32,000+) puzzles have a repeating cut pattern. Their cut presses don’t go larger than 4000 pieces (I think) and so the just use the same cut pattern in the press. If you have a puzzle that is packaged in 4 bags, the cut pattern is 4 identical puzzles (except the edges of course) and you can solve it wrong by not referencing the image. Source: My wife loves large puzzles and got me into it. I haven’t finished a gigantic one yet, I’m still working on the Educa Wildlife (33,600 pieces)
I have never puzzled so hard that I decided the picture on the front of the box was spoilers. Life is a game of putting rules on yourself and that is not one I will apply. Happiness feels cheap but never deciding to be happy feels worse. Nothing will “make you” happy. You just decide you are or you don’t. If you can decide at any moment to give yourself a reason to be happy then the reason is just as cheap. Every feeling has to come with an excuse to have it or a “reason for it” and any reason you make up is valid because nobody can say it’s not valid. So if any reason is valid then none of them matter and you are just making it up. So it’s all made up and fake just like all the rules you use to make it up and fake it. Stop pretending feelings are the goal. Don’t have goals to feel a certain way. If you feel happy for an hour you get tolerance to the chemicals your body has to make that feeling and go numb to them, then if you are sad too long the same thing happens. Being emotional all day every day and rolling from happy to sad to angry and back just to keep feeling all the time is a horrible life destroying addiction. Stop trying to feel every day all day.
Wait, did I miss something? How did Matt have a thumbnail to get turned into a puzzle, that included the puzzle it was going to become. Does he have 3 versions of the thumbnail so the one multiple levels of reality down on the puzzle isn’t the thumbnail…? It’s the Chicken and the Egg all over again and now my brain hurts.
I’d imagine the number of pieces has a lot more to do with the tools available to the manufacturer to create the puzzle. Are they really producing a unique puzzle size and aspect ratio for each puzzle, or do they have several standard sizes, and they adjust the image to fit the standard sizes they’re tooled up for? My guess is the latter, and it’s also possible those standard sizes just vary by manufacturer.
One other thing that’s interesting is that many of these companies use the same die to cut different puzzles, which means they need images of exactly the same size and aspect ratio to make multiple puzzles with (and you can swap pieces from one puzzle to another as a result – Dave Gorman has a really good episode of Modern Life is Goodish looking into this)
At the Disney piece ratio of 1.0074, they could have used exactly square pieces and lie about the size by 0.4cm, or lie about both the height and width by 0.2 cm. (would professional puzzlers be upset of the size was 0.2cm smaller than advertised?) Assuming the size listed on amazon is correct is very optimistic.
If they stretched out the pieces to be too far removed from a square, they’d lose half of the possible orientation for each piece. And now we need a puzzle that has deliberately varying size ratios for each piece just to rub it in. Also it’s kinda ironic that the designer of a Monopoly puzzle would go to those lengths (literally, pun not intended) to avoid giving you more pieces than advertised
How long would it take to solve a 10 x 10 puzzle that had no “edge” pieces, and each piece had only one piece that could fit each unique side? You dont know which pieces are the edge pieces, and the completed puzzle is just one solid color. Its purely trial and error. Suppose it takes one second to try each piece. Like if you are down to the final 20 pieces, and you try one piece in each possible location and it takes one second for each try. Any attempt to match any piece takes one second. Is there a way to calculate this? I dont know the word for it, but i think there is some calculation for the most probable number of trials before you match any two pieces together given the number of possibilities which probably constantly changes as you have fewer and fewer unmatched pieces. Thats my challenge. Love this channe
Don’t you feel a need to use your new dataset to estimate the most likely parameters for your objective function? There’s a nice opportunity for some Bayesian statistics there. Maybe you could crowdsource more puzzle counts from the jigsaw websites, and include the manufacturer in the dataset in case different manufacturers have different capabilities.
I see a problem with second hand puzzles. If the person selling the puzzle (charity shop, ebay etc…) checked and counted the pieces and had the exact number stated on the box, there could be a chance there are pieces missing. It seems a bit naughty that they don’t give the number of pieces stated, even if it is more.