Why don't Jigsaw Puzzles have the correct number of pieces?

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 😮

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!"

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

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 :)

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.

Matt's got me thinking, "A 1.6 piece ratio! Outrageous!!!", even when the concept didn't even exist to me 20 minutes ago.

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.

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

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

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.

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 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 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

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.

It's understandable, Matt. All programmers run into off-by-one errors occasionally. Most of them do while programming, though.

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.

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.

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)

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.

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.