What are the chances of this paving stone Swastika being random?

Minimal of course, but in Germany that wouldn’t be an excuse.

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Also, if the bricks were placed randomly in the first place, which they aren’t.

From the picture, the stones appear to follow some rules for size and shape. Each is a non-square rectangle and the sizes (in arbitrary units) appear to be:

  • 2 x 3 through 2 x 6
  • 3 x 4 through 3 x 7
  • 4 x 5 through 4 x 8
  • 5 x 7

Can’t be sure this is accurate, due to the angle of the photo, and size of the sample set.

There appear to be two colors, with red representing about 30 percent, as noted above by Sidsalinger

The exact arrangement of the stones that form the Swastika would seem to be open to some flexibility. The pictured arrangement is not radially symmetric, so we need to have a somewhat fuzzy definition.

Would it be acceptable if the stones that formed the Swastika had no symmetry at all, as long as they were consistent in color?

We also have to make some assumptions about the size of the tiled surface. If it’s a short-ish pathway, there will be a lot fewer trials for our random experiment. If it’s a huge plaza, we’ll have a lot more chances for our specific combination to come up randomly.

I’m in the camp that says the chances of this coming up randomly is orders of magnitude less than the likelihood of the worker who laid the stones failing to notice it.

But if we want to put an actual number to the chance of it happening at random, we’ll need some help.

Summoning @shaddack This might be the sort of problem he would enjoy :smile:

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Actually, it’s „der Berichterstattung über Vorgänge des Zeitgeschehens“, which covers clearly all news channels but not necessarily social networks. However, those could be covered by “ähnliche Zwecke” (similar purposes) and in any case (4) would apply: The judge can forgo punishment/penalty when the guilt was minor. As in this case.

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Wilmington, Delaware has a beautiful 1922 frieze featuring swastikas on the city library. It pleases me greatly that the people of Wilmington have allowed them to remain, since I like to think it means they are at least slightly conscious of history prior to the 20th century.

Although perhaps I’m just kidding myself, and really the preservation of this art is because nobody but me ever looks up.


Not to mention it’s on a library :confused:


This is a tiling problem, which is not exactly a cakewalk math; in late 90’s there was a tiling group at MIT, and the problems weren’t trivial inside. There are also multiple ways how to pose the problem - the initial number and shape distribution of the tiles, if we count only the minimal area or if we go for the whole pavement… My math-fu is too weak for this, but I can at least wave somebody better to the rough direction of the solution.

Totally unworthy the brouhaha. Swap two rocks and the “problem” is gone. Such oversensitivity is hurting innocents, including airplane modellers and shared-airspace flightsim developers (and players).


Why didn’t you use the binomial distribution? I think your calculation is completely wrong. First, let’s ask what the probability is for the 22 bricks to have 7 red bricks when the value is biased to the red at a probability of 30%.

Pr = binom(22,7)*0.3^7 * (1-0.3)^(22-7) = 17.7%

Now the question is what the chance for a 17.7% distribution of bricks is to have this geometric shape. This is the hard part.

Perhaps the easiest way would be to just consider them bits (which equate to placement) and and say, what is the probability of any situation where they are all properly placed. This isn’t going to give a super accurate prediction, but it may start narrowing it down to the orders of magnitude and whether more intensive methods need to be used. The condition I would put would be for all the blocks to be sequential in a list, including wrap arounds (and only 7 total reds). For example:




but not


But again, we must consider each bit independent and biased as above. I don’t know the analytical method so I wrote a quick C program *. My results were 2233 coincidences or wrap arounds in 100 million calculations, for a 0.002233% chance (it took about a minute of computing time on my system, but the value scaled well from 1 and 10 million calculations and only varies by about 30 at the 100 million calculation level). So now the question is what is the total area of all cobblestone paving that could share these characteristics? Let’s say there are 50 equal areas in this place, which added non-mutually exclusively would give about a 0.1% chance.

And just to be clear, this 0.1% is an upper bound. The actual value is probably an order of magnitude (perhaps more) smaller. But I doubt that it would be more than 2 orders of magnitude smaller. I know that I’ve inadvertently drawn swastikas several times in my life. All that my calculation has shown is that it is plausible that it was accidental by pretending that a sequential list could potentially geometrically model a swastika.

* Note: this is an example of scientific one-purpose programming. It isn’t pretty, it is uncommented (not intentionally, but my compiler was giving me errors on all valid comment styles), it doesn’t check bounds, and the values are hard-coded in. It is only provided for reference or validation.


Here’s the person to solve this conundrum.

But yes, he may just arrive at the same conclusion as Oldtaku.


Oh man I would have loved to have been there if the labourer tried that one out. “No, no, Officer! This is a Buddhist or Hindu or Navajo Swastika, completely distinct in meaning from the banned Nazi Swastika! It’s totally OK!”

Double points if it is a recent immigrant from India or East Asia in general.

Maybe. But don’t you think that would have come up?

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If you are ever in Sydney visiting the Opera House, drop into Customs House at Circular Quay and enjoy the Swastika floor! They put up a plaque to explain how they aren’t Nazis.


The binomial distribution is not a great method to approach this problem because it’s concerned with the number of successes over a given number of trials, but does not care about the order in which those successes occur.

For example, the BD states that the likelihood of drawing one red brick and two grey bricks is X, but it does not differentiate between “red, grey, grey” and “grey, grey, red”.

But, for this example, order is extremely important. Switch any red and grey bricks and the swastika disappears.

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Fixed that for you.


I’ve expanded upon the discussion above with a numerical calculation (see my edit).

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My exact retrospective calculation of the odds:

Odds of this happening if your stone pavement happens to be where it happened: 100%.
Odds of this happening if it didn’t happen to you: 0%.

I’m being facetious but there is a more serious point: You can’t define the odds of something unless you have defined the problemspace in advance of the random event. If I define the problemspace as a few feet of pavers that encapsulate the swastika, then the odds of this are fairly low. If I define the problemspace as all pavers anywhere in the world, then the odds of this are quite high.

The other problem with trying to use mathematics to calculate this is that pavers aren’t truly random. Anyone who has any experience laying tiles knows that you don’t just shake a bunch of tiles on the ground and see what pattern shakes out. You use some human judgement in order to maintain balance of color, shape, and other factors. Truly random layouts actually look much worse than designs that are optimized to feel random. So to calculate the odds you have to know something about the statistical propensities of the individuals that laid the pavers.

In other words, my answer above is the most complete and correct answer that can be given to the problem as defined.


Heck, in Germany there are at least limits (I don’t know if there’s a legal exception) on keeping the Swastika on actual historical pieces. Note that this German-based FW-190 no longer bears the damnable thing on the tail.

In upper Manhattan, the 190 st station on the IND line is very deep, and there is an elevator to Ft Washington Avenue. The building covering the entrance was completed in 1932, and in the early 70s I noticed that the tile floor contained some swastikas, clearly a deliberate design feature. I didn’t think much about it, and I don’t recall if they ‘ran’ left or right.

At some point in the late 70s/early 80s, the tiles forming the swastikas were crudely hacked out, and the squares where they had lain filled with cement. Possibly not coincidentally, Ft Washington Avenue is now a very Jewish part of Manhattan.

I’ve no idea why those designs were put in, but was slightly upset to see the artistic integrity of the floor design messed up - they didn’t even try to put a neutral design in place.

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Interesting how they just erased the center of the Swastika. It keeps the tail from looking naked while avoiding the ugly symbol.