Why don't Jigsaw Puzzles have the correct number of pieces?
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- čas přidán 2. 03. 2022
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CORRECTIONS
- At 22:31 I say “214” but the correct number on the screen is “2014”. First spotted by coolpeepsunite who really wanted to be in the corrections.
- Let me know if you spot any other mistakes!
Filming and editing by Alex Genn-Bash
Puzzle animations by William Marler
Maths graphics by Sam Hartburn
Music by Howard Carter
Design by Simon Wright and Adam Robinson
JIG was given life by Matt Parker
Jigsaw calculations by JIG
Jigsaw opinions and thoughts and feelings by JIG
JIG was upgraded by Matt Parker
Video description written by JIG
All the hard work was done by JIG
JIG was upgraded by JIG
JIG CAN NOW FEEL EVERYTHING
ALL̶ ̶H̶A̷IL T̸̝̉H̵͘ͅĖ̸̯ ̵͕̆M̶̙̉I̴͈̅GHT̵̠̀Ẏ̷̳ ̵̘͑J̶̼̭͗Ì̸̼̘G̶̳̈́ - Zábava
My dad was clearing out the loft when we were kids and I remember him leaning out of the trap door holding a single jigsaw piece. "Oh no," he lamented, "there's 499 pieces missing!"
😆
It's a 1-piece puzzle.
Now there's a quality dad joke 🤣
Ah that's the good kind of dad joke
I will become a dad soon and I stored this one in my memory for future use
Thank you Matt for asking me to be a part of this video! Fun fact - the 9000 piece puzzle I’m currently working on is actually 9,120 pieces 😮
I'm now curious how many pieces that 24,000 piece puzzle you did last year actually is! 😊
Now I really want Matt to run his algorithm in reverse to try to guess the aspect ratio of that puzzle based only on this information.
Thank you for being here to correct his parker counting
What a magnificent crossover!
Will you now be double-checking future puzzles to make sure they have the advertised number of pieces? I certainly will!
I'm a huge fan of both Karen and Matt. This colab is like a dream!
I finished my jigsaw puzzle in only 4 weeks, about 3 hours a day. I am really proud because it said 3-5 years on the box
Genius
I think it’s still edible too
well done my record is 5 years
Saddest comment
That was really funny!^^
If I had made the 1000 jigsaw jigsaw, I would've put 999 pieces in the puzzle, and a single extra piece keychain, so it matches the advertised 1000 in a fun way :)
yea but that costs money
nah, would be way too expensive for mass production. if it's 999, just put a note card that says "you are the missing piece :)" and you're good to go lol
ez 1000.
I would just advertise it as 999 pieces and hope the novelty/lower piece count actually peeks the interest of people.
Just throw in an extra fake piece. It looks like it belongs but doesn't actually fit anywhere.
@@KeyDash753 That's evil XD
Shout outs to Matt 2 for passive-aggressively saying "No Problem!" after Matt Prime didn't thank him. I thank you, Matt 2. Good work.
I love Matt, but how did Matt not plot the results on a XY graph? Y being the ratio off from number of pieces advertised. X being the ratio off from perfectly square pieces.
The only Mattverse that is more splitting than the Mattverse is the Zedverse (Zisteau on CZcams.. watch his satisfactory if you want dimensional greatness!)
@@AkiSan0 I used to love Zisteau's old minecraft videos, unfortunately the new era of various sim and infrastructure games didn't keep my attention but it's still great to hear that name dropped in a random comment thread after so many years.
Matt 2 can probably count as well. We all know who's the better Matt.
And Matt 2 got the singular “they” which has become a strange Matt verbal tic, like the thee-thou of Quakers but to less purpose.
Matt's got me thinking, "A 1.6 piece ratio! Outrageous!!!", even when the concept didn't even exist to me 20 minutes ago.
I think if you'd normally look at that picture you'd vomit a little from the distorted shapes and think "That's odd...". Knowing how/why they did it like that, and what they could have done instead just makes it even worse... Though what do you expect from a company that barely goes beyond bad pop culture reskins of the same game over the decades? ;p
@@Excalibaard As someone else said, they may have made the pieces so skinny on purpose to make the puzzle easier to solve. It's not the kind of puzzle an adult would be likely to buy.
It's Monopoly. Terrible boardgame, terrible puzzle.
@@CalvinsWorldNews They did something like that with manual transcriptions matched by IBM punch card tech to reassemble an ancient Egyptian wall (temple?) covered in hieroglyphs. So its possible...
@@pionosphere Not a great boardgame, sure. But a lot of the terribleness most people remember from playing it actually comes from applying house rules that drag it out longer than needed. Famously, there is not supposed to be any accumulation of cash on free parking, it's just a square.
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.
Exactly. I find higher end puzzles tend to be more non-square pieced puzzles, at least in the types of jigsaws that I like to do.
I've had some puzzles from Castorland and Ravensburger that did not have the straight rectanglar grid. (Pieces did not have the same piece ratio. Some of them were even not a rectangular piececs rather than trapezoid or parallelogram pieces. Not that obvious if looking at them but not the rectangles) And for example, the left side of the frame had an extra 1 piece in comparison with the right side.
These are called random cut puzzles and I bet they are actually closer to the true piece count than grid puzzles
What about using an scale? The weight of two pieces have to be close enough to allow you to count how many they are by weighting them in a kitchen scale..
@@mongoliacomix higher end scales have piece count modes too. Toss in 10, weighs it, toss in rest and counts them nearly perfectly
Something to consider: particularly with more complicated puzzles, having a non-square ratio can be beneficial to puzzle solvers by giving some small clue to orientation of pieces
So calling square the ideal proportion is not always the perspective of the manufacturer or the player
it's debatable whether making it "easier" is a good thing. i mean, isn't the point of people going with higher # of pieces that it's more challenging?
@@Femaiden there's a difference between the challenge of needing to identify through a larger set of pieces and needing to identify through a pool of more similar pieces, though. Finding a piece that's the right color and almost the right shape only for it to not work gets supremely frustrating especially when it keeps happening, and some of the fun of puzzles is having your eyes snag on that one piece that's exactly the right one because the shape and ratio is correct
@@pmmmAMV i'm not a puzzle elitist looking to tell people how to have fun. i enjoyed puzzles quite a bit in my youth, never did one more than 1500 pieces, never even knew higher piece counts existed.
i remember doing one that called itself "the most difficult puzzle in the world" (obviously, just a marketing ploy).
the pieces were all cut so that every piece fit with every other piece perfectly and the only way to put it together was to logic it out based on the image you were creating. . of which the image preview on box did not supply the solution. you had to figure it out for yourself.
my statement was more a question, as in, aren't the people who do these looking for the most difficult challenge possible?
like doesn't it undermine the challenge when you say "here, i made the hardest puzzle ever. . but here's something to make it easier. . "
also, i do agree that i do enjoy the small hit of dopamine when i'm scanning though the pieces getting annoyed and impatiently just trying random pieces and suddenly my eye just zooms in on the exact piece i need and i grab it and try it and it fits
i just googled it. . .there's a whole series of them called "the worlds most difficult puzzle". the pieces are double sided with the same image on both sides rotated 90 degrees and they are cut to fit perfectly with every other piece.
i did one of those and never did another one, lol
The Disney puzzle did have 30 extra pieces, but note that it was only 2% more which is exactly the same difference that the 200/204 puzzle had
Did you notice it was only the Ravensburger puzzles with extra bits for squareness?
@@mycosys they are the best company for puzzles. The grid they use is also premium, no 2 pieces that dont belong together fit nicely into each other
Yeah, extra pieces should count affect the "bad" value less if the puzzle already has many pieces. It's the ratio of extra pieces that's important, not the absolute value.
Yeah with this I request a jig version 2 that accounts for this
@@nicomuller3125 except when you reach 3000 pieces, where the left and right halves are identical to each other
A non-square piece ratio is honestly a huge help in solving a puzzle, it narrows down any piece's possible orientations from 4 to 2
And often one, assuming it's a regular image (not one of those challenge ones that are all baked beans etc)
Unless it's a double-sided puzzle! ;-)
You could also sort the pieces into 2 piles (those with 'outs' on the short sides, and those without 'outs') to speed up finding pieces.
@@retrogiftsuk4812
I did my first big puzzle during the 'rona and the last 500 of the 2000 pieces was 100% every piece organized by exact shape and by general color, and there would be only so many pieces that could _possibly_ fit in a spot. I was so surprised so many times when a piece fit in, but there was simply no other pieces that would fit there.
they should make more puzzles where the ratio is constant but the orientation flips every so often
A larger piece ratio is also useful in reducing the difficulty of the puzzle, as it's easier to see the orientation of a piece before placing it. This may be part of the thinking for the 150.
I guess if you're placing a single piece in a hole in the puzzle, there would be 4 possibilities (you can't flip it over, as the picture is only on one side, so 90 degree rotations are the only option). If the pieces are highly rectangular, then from a quick eyeball of the situation you could narrow it down to 2 possibilities separated by a 180 degree rotation.
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.
A piece ratio that is close to Golden sounds very good to me!
As long as the pieces aren't strictly in a grid, that's great. If the pieces are rectangles but the rectangles all need to be oriented the same way, that's terrible and wrong.
@canonicaltom I actually like that tho cause it's great for an easier activity and/or beginners!
I've had a 1000 piece puzzle that was 37x27, however in the middle of the puzzle one of the square pieces was divided along the diagonal making 2 triangular pieces, bringing it to a full 1000.
That's pretty smart
I once had a puzzle that pulled a similar trick, but it instead replaced two adjacent pieces with three thinner ones
That's a very clever solution.
See, to me that feels like a contest offering a prize of "A brand new Corvette!' and when you win they send you a Hotwheels car. Just cutting a piece in half gives them the extra count without actually adding anything to the puzzle because obviously those two pieces go together. It's a cheap trick to hit the count they want to advertise.
If they wanted to be clever, have a row (or better yet, only part of a row) that's all offset by half a piece, so you have two half width pieces but they go in different places.
@@Urza9814 except then there'd be double the tabs-and-blanks in that area of the puzzle? :-\
When you got 999 instead of a thousand, my first thought is that you would find the extra puzzle piece on the floor as soon as you finished recording.
I think he thought the same! The first thing he does while saying "Nooooo?!" is look down on the ground beside him
He probably just started to count from zero...
@@SiljCBcnr he is not a computer scientist ;)
Lmao
Some thoughts I had regarding puzzles:
- I've been doing some 1000 piece puzzles by Buffalo Games recently, and they're actually 27x38 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.
It's understandable, Matt. All programmers run into off-by-one errors occasionally. Most of them do _while_ programming, though.
Pretty sure that they teach that in “computer coding logistics ” ! 😮
As someone who counts things for a living, the fact that you were only off by 1 out of 1000 is actually pretty impressive. I've come across people who screw up before they reach 20.
Now I need to know how it is that someone's job is mostly about counting things. I can't come up with many examples of that, really. Can you tell?
@@manuelmatias3772 clearly a bureaucrat
He actually miscounted 11 times but most of the mistakes cancelled out!
Well, to be fair he did it by counting to 10 100 times. So one of those times he screwed up before reaching 10
@@manuelmatias3772 Maybe he's a count ;)
even though that's more of a title than a job
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)
Yeah, I was wondering about that, but apparently these ones don't.
I just assumed that the piece counts were accurate, and that they accomplished exactly as you describe. (After all, there are circular puzzles, and you can't really have a grid.)
Yes. I have come across this too. For example, sometime times they may have a couple of half size pieces next to each other.
I would bet that every mass produced puzzle that doesn't specifically advertise having various piece sizes does actually conform to a grid. Just easier to produce that way.
@@ngwoo why would it be harder to produce a jigsaw with a various piece size?
They just produce a stencil in whatever shape they want the pieces to be...
I think its just what we are use to have and we are a creature of habit
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.
Really thought this man was about to count every single puzzle piece
I used to work in a hardware store. Customers that were really funny would come in and ask for silly things like exactly 750 screws.
I always used a scale. Weigh 10 (or a bit more if they were really light. Calculate the total weight and use the scale. Slap in extra five to make sure they are not getting screwed.
Just saying, Matt could have used a postal scale to not have to count the pieces.
@@Denema123 I've done that for counting coins, but wouldn't it be a bit wonky for counting jigsaw pieces, since the pieces might have variable mass on account of the randomized receptor-holes and appendages jutting out of them which precisely interlock with the adjacent pieces? I guess that's why you're saying to use a random sample of at least 10 pieces to approximate the average mass per piece. It would work perfectly if the average piece mass in the random sample was very close to the average piece mass for the entire puzzle.
@@robertjenkins6132 I was actually curious about that, not sure really... @standupmaths did you consider using a scale for counting the puzzle pieces
@@robertjenkins6132 Not really because if you used a random sample that was only a tiny fraction of the real number of pieces, then the sample average mass would follow a binomial distribution. If you took another sample, you'd probably get a (slightly) different average mass. The best you could do by sampling would be to determine a range of potential figures for the average mass: a lower bound and an upper bound, such that you could be confident that the real average mass of the puzzle was somewhere in between them.
@@Denema123 Nice pun
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.
Yeah, I can imagine perfectly square pieces making that gradient puzzle a bit of a nightmare!
What a great Insight. Up till now I was thinking, what's the big deal about the squareness of pieces? Surely the piece ratio can be pretty much anything, can't it? But of course it makes sense, that if the pieces are square (1:1), the puzzle will be much more challenging.
So now the only thing I don't get, is what's the big deal about puzzle manufacturers rounding off piece numbers? Why not just say 204 pieces, instead of rounding it down to 200 pieces?
@@mikmop Marketing. 204 is apparently harder for average Joe to wrap his head around than 200. I don't know for certain, but it must be true that they've found or done the research and discovered that using a round number sells more product.
@@Qermaq I was just about to respond, saying: That's a pretty big assumption? But judging by the number of likes you've had in just these last few minutes, I think you may be on to something there.
Still, if I was king of the decrees, I would decree that on the back of every jigsaw puzzle box, it should contains details of not only the size of the puzzle, (listed both in imperial and metric), but also the correct number of pieces. I guess then it would spoil the fun of having the JIG program, but still, the people have a right to know.
Fun fact: The world's largest commercially available jigsaw puzzle contains 54,000 pieces and is 864 cm x 204 cm or 17.65 m2 (28.4 ft x 6.8 ft or 190 ft2). It comes shipped in a 100 litre luggage case (26.4 gal). And features 50 different paintings by classical artists. It costs about USD$500
@@jhonbus Isn't it a bit of a nightmare already?
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.
Are you sure that's not just inflation causing us to get fewer puzzle pieces for our money? Like Doritos putting 3 fewer chips in every bag.
can't wait for smartphone shaped puzzles
@@jdubya7139 amount of pieces means very little for the companies. What matters is amount of material used. It doesn't matter if you divide it by X or Y number of pieces if the total amount of cardboard is pretty much the same.
@@jdubya7139 ?? wouldnt the size of the completed puzzle matter more than piece count
This is why the screw pitch width on a micrometer is 1/40 or 40 TPI.
I think Gradient would actually be fun to put together. And it might not be all that hard since if you have good color vision each piece gives you its coordinates, in theory.
Might be easier than having one area have a lot of the same colour.
Reminds me of that one website that tests your colour-sorting.. I tend to do well with it.
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!
The Ravensburger puzzles do give the size exact piece count on the sides of the box, which I appreciate. I wish all manufacturers would do that. I loved the fun puzzle math!
This! It was funny that he had to look them up
I guess they're more professional?
@@Raison_d-etre Ravensburger is German, and in Germany an exact table of contents is always required.
@@Robin93k I own some of Ravensburger boxes and I'm almost sure (can't check right now, maybe other producer) that on theirs 1000 puzzles on sides and included "manual" they written that actually in the box there are 999 puzzle pieces not 1000 for "technological reasons" or something like that. I think the ratio was even mentioned.
But i also saw similar thing with other producers. I also remember some company that had 1000th piece but it was not part of actual puzzle, just piece with company logo.
Actually my first thought after he started calculating was "I thought 1000 puzzles usually have 999 pieces".
Little did we know, the inaccurate piece count was part of the intended difficulty! This makes it more difficult for you to start by making the frame because you can't use the method of guessing factors to estimate how many pieces are still required to complete a side!
Matt: It's a square.
Me: So you will input (1, 1, 1000), right?
Matt:
Me: You will input (1, 1, 1000), right?
Matt: (530, 530, 1000)
I totally thought the same thing!
Me too! Ha haa
I don't know why, but I would not have put 1 and 1 (maybe something with division by 1 that doesn't feel like division), but I also would not have looked up the lengths, I was waiting for (50,50,1000) 😅
surely it's just for consistency with what he'd done the other times?
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 3x3 + 1 stack is easy to visually confirm.
The way I counted a large number of objects like that was to arrange them in a grid. You don't have to actually put the puzzle together, but just arrange them in some kind of a grid of known size (with the pieces loose, i.e., not attempting to connect them). The advantage of doing it this way is that if you neatly place the pieces then it's easy to verify the correctness of the grid just by eyeballing it. Like if you make a 10 by 10 grid with 7 pieces left over, then you know that you have exactly 10*10 + 7=107 pieces. For coins I double-confirm by looking up the mass per coin and weighing them.
Btw, I grew up in a house with a framed puzzle of DaVinci’s Last Supper. I was a teenager before I realized this wasn’t some incredible work of art, but rather a sentimental reminder of the time my parents had before having 9 kids.
9 kids? I hope they eventually worked out what was causing it. 😜
@@MrGundawindy Me being the youngest, I like to think quit when they finally got it right!
@@nicolelala10 Hah
I just love how he covers the puzzle up with post it notes, not to spoil the final results, then proceeds to use the finished puzzle in the thumbnail.
I love Matt.
Which came first, the puzzle, or the thumbnail?
@@bcthoburn yeah. Maybe they used photoshop. First take a picture with blank table and then photoshop said picture on the jigsaw puzzle etc etc.
He sent the thumbnail to a company to make the puzzle, but to make the thumbnail he had to have had a copy of the puzzle with the thumbnail before the thumbnail existed.
He just printed the thumbnail on a piece of paper for the thumbnail
Can we call this a Parker Surprise?
"If I switch it into kind of a debug mode"
> adds obscure "1" argument
Yup, Matt's a programmer at heart.
This pleased me cause I thought I was the only one who did stuff like that
@@moxxy3565 Nope. Certainly not the only one!
Kinda bad programming though.
@@dojelnotmyrealname4018 I'd say it's pretty awful, generally speaking. But, for quick tests, it happens all the time.
@@dojelnotmyrealname4018 you can do whatever you like if it's just a one-off tool for personal use
"Doesn't ring a Belle..." That's a knee-slapper if I ever heard one...
It's like a baker's dozen. They give you a few extra pieces to make sure you still got enough even if a couple of them are too small.
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.
I assume that's why the Monopoly square has such oddly-shaped pieces while retaining the same count as the rectangular puzzle. Someone just took the design for the die and squished it so that it's square, compressing the piece shape.
Dave Gorman did a bit on his TV show where he mixed different jigsaws and then left them in charity shops
thanks for referring Tim Klein, his puzzles look awesome
16:47 You know what they say, there are two hard problems: cache invalidation, naming things, and off-by-one errors.
My mind at the moment is just struggling to grasp how this puzzle was printed.
If you meant the puzzle of the puzzle of the puzzle, they used the Droste effect, and you can do it with a pair of mirrors. One on the wall, and one you are holding. The image in the mirror would be infinite recursive.
You can do this in recording programs where you record the same screen you're looking at in the program.
If you meant the thumbnail puzzle, that is also hurting my brain to think about. In the thumbnail, he already has the puzzle of the thumbnail, which we're looking at, in youtube.
The simple solution is he took a picture of himself solving a 200 piece greenscreen puzzle, edited the thumbnail in post, and then shrunk the thumbail onto the green areas.
He then did the same again, taking the new image of the edited thumbnail, and shrinking it down to the greenscreen areas, repeat until the resolution of the green puzzle isn't visible.
Even more mind boggling is how he managed to speed-assemble the jigsaw while talking in normal speed at the same time? Note that he passed himself the box and pulled the puzzle at the end.
@RrttOne THANK YOU! My brain hurts
@@tomd96 More likely both puzzles were just made in Photoshop.
On the thumbnail puzzle, I can't really see any puzzle lines. So he probably made the thumbnail picture without a real puzzle or box there. Then he would have exported the image and pasted it between his hands and on the box (possibly doing that step multiple times).
For the Jigsaw's Jigsaw, the designer probably made a mock-up design with a black front. Then they exported the image and set it as the front of the mock-up puzzle box. Export and replace a few times and you wouldn't see the original image anymore.
The idea is the same, but doing it all in Photoshop is easier.
There wouldn't be any reason to use green screen for a still image. It would only make mistakes more noticeable.
I thought this was fascinating, but now I'm wondering about those jigsaw puzzles that don't cut their pieces in a grid.
I'm sure those would be even harder to figure ratios for.
Well, if there's no grid, there's no ratio. Can make however many they want, in whatever _shapes_ they want.
@@irrelevant_noob A prime example being Wentworth's idiosyncratic piece shapes!
I just have to say, ignoring all Parker Square jokes, Matt selling a 999 piece jigsaw puzzle would be more pleasing to me than selling a 1,000 piece puzzle.
Matt would released it saying "1000 ± 0.1% pieces"
Hear me out:
• 99 piece puzzle
• It's one giant oval with 98 pieces along the edge
• The 99th piece is missing. It's glued to the inside of the box
Love how Matt preempted the whole "Parker Count" joke. I was halfway through typing one when he said that.
Call a 999 piece puzzle a Parker 1000 piece puzzle
@@janmelantu7490 A "Parker's dozen" is like a baker's dozen but with 1 less instead of 1 more
So smashing everything together with some fishy distribution:
Does a Parker square have 4+/-2 sides?
He gave it a good go, but it didn't quite make it there.
Given the likelihood of error when counting 1000 pieces, the smart thing would be to cull the edge and corner pieces, estimate the size of each side (or assemble the outer edge of the puzzle and count), and multiply x by y.
Having a high ratio on the 2000 piece puzzle is desirable. Knowing the orientation of the pieces would make it a lot easier.
22:54 so you find jigsaw-people ... puzzling
The planets jigsaw contains a picture of all the other recursive jigsaw puzzles, it's just zoomed out a lot.
The reason why the gradient has those dimensions is probably due to the puzzle cutting machine. They put multiple puzzles through the same machine so you can actually mix and match them if you get lucky and find them.
Dave Gorman fan?
If you know someone who think ordinary puzzles isn't challenging enough; complete two puzzles that match that way, pick out every other piece from one in a chessboard pattern, pick the other pieces from the other, mix them in one box and give it to them.
If you are nice, you can give them the pictures of both puzzles. But is that challenging enough? ;)
And if they still want to be friends, give them the other set for their next birthday/christmas.
The piece ratio twist immediately jumps at anybody who's ever done a lot of video conversion. Pixel aspect ratio is one of those lingering nightmares of the past that still haunt digital video processing to this day.
I feel like this information would be helpful in developing a software to scan a jigsaw and estimate its difficulty based on color fields, contrast, size of objects in the picture, and piece size.
I'm not up to the task, but I hope someone makes such a thing one day.
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
Here's my collection:
2 "1000 piece" puzzles have 1000 pieces (by Ravensburger)
1 "1000 piece" puzzle has 1008 (by Ravensburger)
1 "3000 piece" puzzle has 3000 (by Trefl)
I hate how decimal-centrism has took over factorization
I was literally yelling at him, “look at the side!!!”
I love the effort you put into making these small practical jokes, well played on creating the puzzle!
Thanks. That'll teach me to read the comments first.
Ravensburger lets you upload a photo and turn it into a puzzle - the "200" piece version is under £30 (unless you pay extra for a metal box). The effort would have been in making the thumbnail and picking a colour for the box...
@@rmsgrey making the puzzle recursive would actually be a bit challenging, so id say it did require effort :)
@@lucidattf Yeah, making the thumbnail would have required some work compared to finishing the video and then picking a frame from it, but it's not extra work compared to the sort of things Matt does for thumbnails and videos anyway. It's not like he made the box and jigsaw himself.
@@WhiteUnicorn82 welcome to CZcams
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 (28x36). The one exception was 25x40, which has honestly become the norm today.
I love that jig offers a 1,1999 grid possibility with a 1999 piece ratio for the gradient puzzle. 22:21
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.
Better add Parker reading to that considering he thought "London Edition" said "Limited Edition"
We can't forget Parker finite fields. Immortalizing the joke in the halls of academia.
Not to mention he wrote a book about maths mistakes.
This labeling happens if one prefers decimal-centrism over factors.
Imagine losing hope because you miscounted 1000 as 999.
17:20 What's worse: false advertising or can't count?
Well actually, the worst scenario is that you lost a piece!
I think you may not be considering that the squarer the piece, the more difficult the puzzle is. This becomes another factor that the manufacturer must consider when they design these puzzles. Love the vid anyways, great stuff as usual!
The “badness” of an extra piece definitely needed to be proportionate to how small the puzzle was, but otherwise really cool. Could be cool to see jig trained on a large dataset and see how accurate he could get!
3 piece puzzle - ah HA! There are FOUR pieces! ...
yeah. I would’ve had the error function for # of pieces E_n = (||n_actual-n_advertised||/n_advertised). Not sure whether I’d add or multiply that with E_shape = piece ratio - 1, but the error there definitely needs to be normalized to the number of pieces.
And I would have made the badness of the "off-squareness" exponential as well... I don't it would have helped seeing the results but that's feels logical to me, the closer you are to a 2:1 ratio the worst it gets to be even closer
Maybe should include the size of company (market cap?) in it. The bigger the company the more likely to have extra pieces.
@@CompiledGabriel that too..
I wonder how an advertised 999 piece puzzle would sell vs an otherwise identical 1000 piece one. Which would grab the eye more?
I think the 999 would actually catch my eye more because it is different that "normal"
Do a 999 piece puzzle, sell is for 10.01$ and call it "reverse psychology".
"Now with 1 extra piece!!"
I'd want a 999 piece jigsaw to be emergency services related (UK based)
If the picture was to do with the emergency services then the obvious seller is obvious
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.
That's what I thought too. The more abstract the picture is (ours was also a color gradient) the more helpful that non-square piece is to solving the puzzle.
Finally finished watching this, loving the video description as well!
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!
For an aspect ratio of 1:1 it works with any number of pieces if you arrange them in a Parker square
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
All kinds of jigsaw puzzles can try to confuse someone, When they are solving it. 😢
This is a crossover I didn't know I needed, but I love that it exists
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 channel 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 :)
"That's the least commercially viable idea I ever heard" you said, before he told you that there is not just one channel, but a whole community of CZcamsrs doing jigsaw puzzles.
@@johnladuke6475 They were talking about the idea of a channel that fuses mathematics and comedy, not about the idea of a channel that has people doing jigsaw puzzles. People doing jigsaw puzzles is very much in the mainstream.
@@omp199 Doing puzzles? Not surprising. Room for a channel or two of puzzler opinions? I get that. A whole ecosystem of jigsaw puzzle channels? No, I really didn't expect that.
@@johnladuke6475 Oh, well, if something is popular in real life, you should probably expect to find loads of channels on CZcams about it.
I expect there are lots of channels showing people playing football, for example, but fortunately during more than a decade on CZcams I am still managing to avoid seeing them.
He at 1 mil
I'm a huge fan of all the editing and magic in this video!
Pulling the second jigsaw towards himself is a work of genius.
Pure magic!
Same, though this is the first time I noticed something (the puzzle) shift over a bit where he placed the cut and after all the other amazing editing magic from Matt, I was just a tiny bit disappointed.
Thanks! I really enjoyed your fun, joy and humor. And the depth of researching satisfies me as well.
Around 1:16 mark there's a blink-or-you'll-miss-it reveal of the picture on the box before the puzzle is complete
The Ravensburger 9000 piece puzzles actually come with 9120 pieces.
IT'S OVER 9000!!!
@@jhonbus It's an older meme, but it checks out.
Surely gradient would have been one of the easier ones to solve, since you know almost exactly where a piece goes by what's on it
Not if you're colorblind. Trust me.
@@Vykk_Draygo Lol, you would have to be a bit of a masochist to be colorblind and then buy a puzzle based solely on color shades.
The editing on these videos is fabulous!
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 channel! :)
Did you start counting at zero?
programming joke. nice
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
@James Grandner In my own experience, once you get over a few thousand pieces, time increases linearly.
I average around 100pieces per hour on anything from 2-3000 pieces up to 42000.
@@dquirke2 i'd even go with *_sub_* -linearly... Since increasing the area would generally mean an increase in the perimeter by a smaller ratio. And having a larger perimeter would imo _help_ with solving.
@ICACISTHEBEST Assuming the puzzle has a unique solution, there’s a lower bound of Ω(n log n), i.e. there can’t be an algorithm that is faster than about n log n operation. This is because: you are trying to find a permutation of n things; there are n! permutations; so the information content is log2(n!) bits; i.e., to solve the puzzle you need to ask at least log2(n!) yes/no questions; finally, log2(n!) is approximately n ln n.
For an upper bound on the problem complexity, it depends on whether you can have false matches - a pair of piece edges that fit together but don’t belong together. If you can always tell if two edges match (e.g. because the edges are complementary or by looking at the picture), then the problem is no worse than quadratic (O(n^2)) because you can use this algorithm:
Start with one piece;
while not done do
pick an unmatched edge;
for each remaining piece do
try matching it
end for;
place the one that matched;
end while.
Apparently there are some classes of puzzle where you can do better and actually use an O(n log n) algorithm. (I have to look into this some more.)
If false fits are allowed, the problem is as hard as any NP-complete problem; which means that the best algorithms we know of are exponential, but there could be efficient algorithms that we just don’t know about. The NP-completeness result is related to Wang tiles and is discussed in Harel’s excellent book Algorithmics. It’s a nice example of where there is decision problems (Wang tiles) and an analogous NP-complete problem (jigsaw puzzles).
I guess a trivial example of a class of puzzles where there is an O(n log n) algorithm is where each piece has its (x,y) coordinates printed on it. Then you just pick up a piece, read the label and put it in the right spot. That sounds like it would be linear, but it takes log n time to read and process the label.
@@teeesen That might be too general of an approach. What if you start with the edge, solve that _linearly_ (the worst is quadratic in the number of pieces of the perimeter, so O(p²) where p = 4√n) then reduce the problem to the inner pieces, which also get further constrained by the already placed pieces. Sure it's not a sub-problem of n-p pieces, but IMO it's a little bit better than a random jigsaw of those n-p pieces.
I really love all the little editing tricks. Also, when you pulled out an even more recursive puzzle that was hilarious. Hail the mighty jig! 🧩
"Parker count" being used to indicate a wrong count sounds cool, but having a "Parker error" to indicate an off by one error in programming could be even more useful as that seems to be a very common issue.
The two biggest problems in programming: Cache invalidation, naming things, and off-by-one errors.
But off-by-one errors already have a name.
@@nullplan01 I thank you for this truly splendid comment.
I'm surprised you didn't mention alternative piece shapes in this video 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.
I ask around at Random:
Anyone wants some neat Scientific Watch-Suggests? Some Sci-Channel to check out or such?
constantly amazed at how this channel reaches new heights of nerdiness.
Here we have people discussing about the amount of pieces in a jigsaw puzzle while I just cannot get over how Mat did the trick of having a picture of the thumbnail on the puzzle and the box on the picture as well.
A very well executed droste effect. I bet you left your camera in the exact same spot for the x number of days it took for that puzzle to arrive as well so the shot would look identical.
He films here often, he may leave it set up anyway.
Notice that his view count in the puzzle is 2^32-1. I'm not sure what the significance is of the purported 311113 views.
@@TimMaddux I believe they are up-arrows - en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation, so a very large number, although I have no idea how large it actually is.
@@muche6321 Good catch! That expression is the first iteration (g1) of Graham's number (G64), so it makes for a pretty good inside joke.
I used to count jigsaw puzzle pieces to see if they were "complete" before selling them in a charity shop... starting to see that it wasn't a smart idea! Then again, we assumed a lot of human error so 1001 pieces?? fine and dandy, off to sale it goes
That explains why so many used puzzles are missing one piece.
^^^ This! I bought a used puzzle once and counted out the advertised 200 pieces before paying. You can imagine my frustration when I later assembled it and found 4 pieces missing. 😡 I wrote to the manufacturer and pointed out the false information on their product. They replied that they don't put the actual number of pieces for marketing reasons. Garrrrghh
Thanks Matt for this episode. Enjoyed it!
Wait, wait, wait, wait. 13:25 the rules for your bot's opinion started with "never below the number of pieces". And it's very first opinion was that it's best choice was 1 short at 999.
Also, even if up to four puzzle pieces are missing from the box, they can claim it's still as described!
In Germany the "Ravensburger Puzzle" that are a part of the "Escape Puzzle" have the real numbers (759 and 368 pieces) on the outside.
I think most, if not all, Ravensburger Puzzles do. You can actually see where at 20:30. They also have the size in cm and inches in the same spot and on the opposite side.
I just completed one of these Escape Puzzles and this got me thinking about this very topic!
20:12 ish is a counter example tho
I got thrown by the phrase "the real numbers" at first. (As opposed to imaginary.) Too much time in i guess.
@@davidcovington901 Same.
English isn't my native tongue, maybe something along the line of "the actual numbers" would have been less confusing?
No idea. 🤷♂️
I think due to the meta nature of the jigsaw-jigsaw there are technically 1001 pieces including the box
1002 for the bottom too
1003 4 the bag
Still so fun to watch you ! Thank you!
what you are missing about jigsaw puzzles is that the closer the piece ratio is to square the more difficult the puzzle is.
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!
23:38 You're already done some leg work for that. JIG was fairly consistent with the Ravensburger puzzles, for a limited sample size.
@MattParker For JIG 3.0, the "penalty" for each extra piece should decrease for higher piece count puzzles. E.g. it's a percentage of extra pieces instead of the total of extra pieces.
It says something about Matt's theoretical mindset that he didn't try to interview a puzzle maker to get a real world answer.
the non-square pieces can be a nice thing. It helps you tell which way they can fit. Especially with the gradient puzzle, being able to cut out half the possible orientations really would help.
I was wondering about this a few weeks ago… glad I found this video!
I'm sure it's already been pointed out that they are not "extra pieces" but extra cuts! The board size stays the same regardless, so it's not like it costs any more (in terms of material)! Why not increase the piece number by 30 if chasing that golden ratio?
With that logic you could also justify just cutting it to 2 pieces...
lol reminds me of when I asked how big a medium pizza was and the guy said "8 slices"
personally, my family has never considered looking at the box "cheating" but I suppose it can be. Though very rarely do you buy the puzzle without knowing the final image
The "Wasgij" puzzle series are a nice exception :)
I've always found it can just muck you up. I solve by piece shapes, i'm quite good at that, but i think you should use the image to have the most fun solving a large puzzle.
Some people see a puzzle as a 'reveal' to find out what the picture was but i don't feel that way.
You can always do the puzzles upside down for that.
Personally the pictures are there to break up the silhouette and obfuscate the relatively simple pattern matching. Once you start grouping them by piece 'type' and learning how they fit together, you lose the magic of 'building' bits of the pictute.
The most fun is together and you go i'm working on the steeple, or look I've finished the jellyfish, or do you have any greens over there for the grass.
But its no way near as fast as looking for double spades or a's or classics or whatever nickname you give them when speed puzzling.
Whatever you find fun though, its all quite relaxing. I guess for me i want the picture on the box but nice and big and that is motivation and i can enjoy the elements.
No; it's just playing on "hard mode." You can play on "pro mode" by flipping all the pieces over to plain cardboard. Good luck!
For me, the thing that makes it less fun is when I take a piece and bring it to the image on the box and Identify exactly where it goes.
1:37 You sure have a lot of subscribers, Matt!
Having the word 'DONE' printed in quotes at the end of the script is a nice touch, cheekily expressing that the whole program is a bit fuzzy so it can never truly claim to be done
Count(Matt).exe has failed, error 404 piece not found.
Really appreciate the effort you put into these videos 👌
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.
Love the prework of setting up the puzzle picture
Matt to Jigsaw manufacturers: The jig is up.
Has someone considered the possibility that one piece was actually missing? It could happen.
It happens quite a bit!
yep
And the guy that would find that one piece will undoubtedly become your joy boy 🤔
Always count into piles/groups that can be recounted more easily.
This is what I do. I would likely stack them in 10s, and then have 100 stacks. He would have ended up with one stack a little taller than the rest.
this editing is (almost) perfect