The density of waffle syrup went down compared to the 16 partition waffle though
this post was submitted on 04 Mar 2026
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I wonder how many people would have understood both references just a few years ago. Yet today, not only someone made a meme out of this, but it also gets a good deal of upvotes. That's the internet culture I love!
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(8 replies)
The sub-game where you supplex monks was pretty good too.
For the uninitiated: this is the current most-efficient method found of packing 17 unit squares inside another square. You may not like it, but this is what peak efficiency looks like.
(Of course, 16 squares has a packing coefficient of 4, compared to this arrangement's 4.675, so this is just what peak efficiency looks like for 17 squares)
Edit: For the record, since this blew up, a tiny nitpick in my own explanation above: a smaller value of the packing coefficient is not actually what makes it more efficient (as it is simply the ratio of the larger square's side to the sides of the smaller squares). The optimal efficiency (zero interstitial space) is achieved when the packing coefficient is precisely equal to the square root of the number of smaller squares. Hence why the case of n=25, with a packing coefficient of 5, is actually more efficient than this packing of n=17, with a packing coefficient of 4.675. Since sqrt(25)=5, that case is a perfectly efficient packing, equal to the case of n=16 with coefficient of 4. Since sqrt(17)=4.123, this packing above is not perfectly efficient, leaving interstices. Obviously. This also means that we may yet find a packing for n=17 with a packing coefficient closer to sqrt(17), which would be an interesting breakthrough, but more important are the questions "is it possible to prove that a given packing is the most efficient possible packing for that value of n" and "does there exist a general rule which produces the most efficient possible packing for any given value of n unit squares?"
But you can fit 25 squares into the same space. This isn't efficiency, it's just wasted space and bad planning.
You raised the packing coefficient by ⅝ to squeeze one extra square in with all that wasted space, so don't argue that 25 squares has a packing coefficient of 5. Another ⅜ will get you an extra 8 squares, and no wasted space.
Precisely. That's why I wrote the parenthetical about the greater efficiency of 16 as a perfect square. As the other commenter pointed out, this is a meme. This is only the most efficient packing method for 17 squares. It's the packing efficiency equivalent of the spinal tap "this one goes to 11" quote.
My autistic ass can't comprehend why anyone would want to arrange a prime number in a square pattern...
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For 25 squares of size 1x1 you'd need a square of size 5x5. The square into which 17 1x1 squares fit is smaller than 5x5, so you can't fit 25 squares into it.
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Thank you I was very lost lmao
Isn't this only true if the outer square's size is not an integer multiple of the inner square's size? Meaning, if you have to do this to your waffle iron, you simply chose the dimensions poorly.
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Oh my God, I fucking love this. I mean, I absolutely hate that this is the optimal way to pack 17 squares into a larger square such that the size of the larger square is minimised. However, I love that someone went to the effort of making a waffle iron plate for this. High effort shitposts like this give me life
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Where does this picture come from? Is it real? Ive just thought at how absurd an orangutan on a bike chasing a kid actually is.
that bike is absolutely not part of the picture tho
I'm cooked. It looked real
What makes the lower suboptimal?
Since a link to a wiki article does not an explanation make:
The optimal efficiency (zero interstitial space) is achieved when the ratio of the side length of the larger square to the sides of the shorter squares (let's call it the "packing coefficient") is precisely equal to the square root of the number of smaller squares. Hence why the case of n=25, with a packing coefficient of 5, is actually more efficient than the packing of n=17 given in the waffle iron, with a packing coefficient of 4.675. Since sqrt(25)=5, that case is a perfectly efficient packing, equivalent to the case of n=16 with coefficient of 4. Since sqrt(17)=4.123, the waffle packing (represented by the orangutan) above is not perfectly efficient, leaving interstices. However, the packing coefficient of the suboptimal solution (represented by the girl) is actually 4.707, slightly further from sqrt(17), and thus less efficient, leaving greater wasted interstitial space.
Trying to understand what this actually means. Since these two diagrams have the same number of squares, does this mean the inefficient packing squares are actually slightly smaller in a way that's difficult to observe?
Ah, no, it's that the more efficient packing takes up less space, so the less efficient square is actually slightly larger than the other, compared to the smaller squares.
If the smaller squares are identical in both sets, then the larger square in the less-efficient set will be slightly bigger than the larger square in the more efficient set.
wanna maximize syrup? just make it a giant one-square cup.
My nephew just drinks the syrup from the bottle.
How Alton Brown makes his waffles
where can i buy one
This makes me so angry for reasons I can’t articulate
This actually makes me unreasonably happy, kinda like knowing the secrets of the number 37, which is coincidentally your current number of upvotes.
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I'm pretty sure that waffle could easily fit 5 rows of 5, am I crazy?
It's still funny
In the "optimal packing" scenario, it's slightly too small - like 4.95x4.95
It's only more efficient when the containing square is large enough that there would be wasted space on the edges if the inner squares were lined up as a grid. The outer square of the waffle iron is almost but not quite large enough to fit a 4x5 grid. People losing their minds over this weird configuration being "more efficient" think it's because it's more efficient than a grid where all the space is used, which is not what this would be.
the joke is about achieving max density of the squares, density as in square per area of the waffle
of course you can make the whole waffle bigger, but it would decrease the density
a better solution is adding smaller squares though
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To be honest I would love a waffle maker like this where some parts of the waffle are a little undercooked and other parts crispy.
Related:
https://en.wikipedia.org/wiki/Square_packing
Nature is a lot more elegant with spheres:
https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres
I am sad because these squares look very out of place, unlike hexagons which are beautiful and perfect and never cause problems whatsoever, ever ever!
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