## Leonhard Euler

Everything about Sudoku that doesn't fit in one of the other sections
tso wrote:I believe it is possible to construct a 9x9 Graeco-Latin square. For any size that can be made, there will be only a tiny fraction of how many Latin squares there are. I'd guess that far fewer clues would be needed for a unique solution.

http://forum.enjoysudoku.com/viewtopic.php?t=575&highlight=
tinfoil

Posts: 16
Joined: 06 June 2005

dukuso wrote:agreed that he didn't invent sudoku. OK ?
nor did he invent Latin Squares (though maybe was the first to
use that name ?)

No, he never used that name. He wrote in Latin.

dukuso wrote:but he has worked on similar things, so there is some connection. OK ?

Only between Latin Squares and Sukoku, not Euler and Sudoku. Many people, before and after Euler, worked on or with Latin Squares. It's simple logic:

If A => B
and if B => C,
then A => C.

BUT,

If A => B
and A => C
we can say NOTHING about the relationship between B and C!

A = Latin Squares
B = all of Euler's work with Latin Squares including, but not limited to, Graeco-Latin Squares.
C = Sudoku.

If Euler had never lived, it wouldn't make Sudoku more or less likely to have come into being.
tso

Posts: 798
Joined: 22 June 2005

but "connection" is symmetric.
So A connected with B then B connected with A
dukuso

Posts: 479
Joined: 25 June 2005

dukuso wrote:but "connection" is symmetric.
So A connected with B then B connected with A

Yikes! No one said anything about "connection"!

A => B is short hand for A implies or leads to B -- just the way it has been used in hundreds of posts in this forum.

1) The first known example of the Latin Square was in the 1200's,

2) THEN Euler used them in the 1700's to develop the Graeco-Latin square. He conjectured that a 10x10 Graeco-Latin Square was impossible.

3) THEN in 1959, Parker, Bose and Shrikhande constructed a 10x10 Graeco-Latin square, disproving the conjecture. http://buzzard.ups.edu/squares.html

4) THEN some college dropout named "Joey" in Australia took used the design of a 10x10 Graeco-Latin square in his clothing line, including bitchin' beach towels which could also be used as checkerboards.

5) A few years later, Number Place puzzles, based to some degree on Latin Squares, were invented in the US and soon thereafter, were introduced in slightly modified form in Japan with the name Sudoku.

6) THEREFORE, using your logic and that of most major newspapers, the Japanese didn't invent Sudoku, JOE did.
tso

Posts: 798
Joined: 22 June 2005

tso wrote:
Yikes! No one said anything about "connection"!

OK, you used "connection" in another thread.
("There is NO connection between Euler and Sudoku or Number Place")

Here you used "relationship", it's also symmetric.
dukuso

Posts: 479
Joined: 25 June 2005

dukuso wrote:OK, you used "connection" in another thread.
("There is NO connection between Euler and Sudoku or Number Place")

Here you used "relationship", it's also symmetric.

Are you saying that you are still unconvinced, that you still believe that Euler deserves to be mentioned in a history of Suodku? If you wrote an article about the evolution of Sudoku today, would you still mention Euler? If so, on what basis? Which of my arguements do you disagree? If you simply disagree with me on facts -- that's fine. If you think the Euler archive is a fraud, ok, I give. But if you agree to the facts, the logic is iron clad.

Yes, I used the word "relationship" in this thread once. I said:

If A => B
and A => C
we can say NOTHING about the relationship between B and C!

If Latin Squares lead to Graeco Latin Squares and if Latin Squares also lead to Sudoko then we can say NOTHING about the relationship betweed Graeco Latin Squares and Sudoku.

Neither "relationship" nor "connection" imply symmetry. If A causes B that does not mean B causes A.

If you want to use the broadest interpretation of "related" and "connected", then yes, we can draw a connection from Sudoku, to Latin Squares, to Graeco Latin Squares, to Euler. It is a connection without meaning, as we could go on to connect every mathemation and puzzlist who ever lived with equal force. It's like playing "six degrees of separation" or "Kevin Bacon Game". (If you're not familiar with any of these -- please search the web. We're far afield from the topic of Sudoku as it is.)

There are enough documented facts in evidence to support the conclusion that Euler has zilch to do with Number Place or Sudoku. Until at least a *scrap* of evidence contradicting this is found, the matter is settled.
tso

Posts: 798
Joined: 22 June 2005

I sent this email to Euler Archive:

In the last year or two, a graphic logic puzzle called "Sudoku" aka "Number Place" has become very popular worldwide, a puzzle which is based in on a subset of Latin Squares. Scores of newspaper articles and websites have been making claims that I believe to be false, including, but not limited to:

a) Euler invented or discovered Latin Squares.
b) Euler was the first to call them "Latin Squares".
c) Euler introduced Latin Squares to the public at large as a puzzle.
d) Euler's work "A New Species of Magic Square" was about Latin Squares (rather than Graeco-Latin Squares).
e) Euler invented Sudoku.

Am I right in my belief that a through e are false? Would you agree that as brilliant a mathematician as Euler was, he has nothing to do with the evolution of this puzzle and that a history of Sudoku shouldn't mention him?

The manager of the Euler Archive responds:

Thanks for your message. I confess that I have mixed feelings about these questions. I would like to see Euler credited with all that is his due, but in this case I feel like you are correct; Euler did not invent Sudoku. Let me respond to your statements below:

a) Euler wrote the first (to my knowledge) "real" mathematics paper to treat Latin squares in 1776. This was E795, De Quadratis Magicis, and you can find both the original paper and a translation on The Euler Archive. Latin squares have been known, however, since at least medieval times. Indeed, Arabic Manuscripts from the 13th Century sometimes feature Latin squares, and they are often given mystical of Kabblahlic significance.

b) Actually, I think this one is true. The name came up in Euler's only other paper about Latin Squares, E530"Recherches sur une nouvelle espece de quarre magique" (or "Investigations on A New Species of Magic Square"). Euler put Latin letters into a grid, and called it a Latin square. Later, when he added Greek letters, he called it (of course) a Greco-Latin square.

c) You are correct. This is completely false.

d) Again, this is false. Or at least mostly false. The paper is about Greco-Latin squares, but Latin squares come up quite a bit, of course. In E530 he considers diffferent types of Latin squares, and then looks at whether they can be "completed" (that is, made into a Greco-Latin square).

e) Again, completely false.

So continue spreading the gospel of Euler -- it's a travesty that such an influential scientist and mathematician should not be a household name. At the same time, feel free to quash all myths about Euler's inventing Sudoku. =)

So it turns out, Euler may have been the first one to call them "Latin Squares", so I was wrong on that one.
tso

Posts: 798
Joined: 22 June 2005

tso,
Thanks for sharing that info. It would be interesting to see photo-reproductions of some of those Latin Squares from 13th century Arabic manuscripts. (Not that it's likely, but wouldn't it be funny if any were also sudoku grids? )
r.e.s.

Posts: 337
Joined: 31 August 2005

Tso,

I visited some other sudoku webpages in the meantime
and now I understand you a bit better.
Yes, it seems to me that Euler is "overrepresented"
usually there.
I was just attended when you put it into the other extreme
by saying there were absolutely NO connection.

When someone uses "connection" or "relationship"
in connection with sudokus or whatever , then I think we can
usually imply that he has a symmetric meaning of these words in mind.
Of course, anything is somehow related to anything else,
but someting more and something less
(uh, does it make sense ? not that someone picks this
sentence and puts it into a list of jokes or such)
Well, Tso is maybe closer related to sudokus than Euler, though ;-)

It could still happen that someone will find an old letter,
which refers to Euler's paper, and which deals with
sudokus. They could even have printed some sudokus for public
amusement but were not very successful.

-Guenter.
Last edited by dukuso on Wed Sep 21, 2005 5:17 am, edited 1 time in total.
dukuso

Posts: 479
Joined: 25 June 2005

This manuscript at the U.S. National Library of Medicine shows a Latin square in the margin of a Persian copy of the Kifayah-i Mujahidiyah, an Islamic medical treatise from around 1385. This copy was written in 1552, but the Latin square is one of several said to have been "added by later readers". Here's a snippet:

As you can see, the Latin square is a 4x4 Sudoku grid!
r.e.s.

Posts: 337
Joined: 31 August 2005

dukuso wrote:Tso,

I visited some other sudoku webpages in the meantime
and now I understand you a bit better.
Yes, it seems to me that Euler is "overrepresented"
usually there.
I was just attended when you put it into the other extreme
by saying there were absolutely NO connection.

Must I drag Euler from the grave to refute you?

Sudoku are NOT based in any way, shape or form on ANY of the fruits of Euler's labor. If he never existed, there is NO evidence that suggests that Sudoku wouldn't exist in exactly the same form. Belief without evidence isn't science -- it's religion. If you simply have faith that Euler was involved some how, there no sense in debating.

If I poison the water tower, every one in town will become ill. If I poison MY tap water, you will be unaffected. The fact that water comes into my house through a pipe that is ultimately connected to the water tower in NO PRACTICAL WAY connects me to you simply because you also get water from the tower.

dukuso wrote:When someone uses "connection" or "relationship"
in connection with sudokus or whatever , then I think we can
usually imply that he has a symmetric meaning of these words in mind.

No, we can't infer that at all. Few relationships are symmetrical. You might know the Queen of England -- she does not know you.

dukuso wrote:It could still happen that someone will find an old letter,
which refers to Euler's paper, and which deals with
sudokus. They could even have printed some sudokus for public
amusement but were not very successful.

That's ridiculous! You could just as well hope to find "an old letter" written by Euclid describing Sudoku exactly! Maybe Pythagoras authored a lost manuscript that describes the Rubik's cube exactly, but unless and until we find it -- or at the very least, find some evidence that even suggests that it might exist -- we'll have to assume that Erno Rubik is the rightful inventor of the Cube. An argument like that is irrefutable -- and has carries no weight.

In my opinion ...

... if you look at the work Euler did in this area, you will see that he used existing latin squares as a building block. He's no more responsible for their creation or they're popularity than he is for the latin and greek letters that he used.

... I mentioned this elsewhere, but the simple latin square is too simple to ascribe to *any* inventor or discoverer. I'd be surprised if you yourself didn't scribble something like this in your notebook while in grade school:

Code: Select all
`1234234134124123`

Would we try to find the inventor of this sequence: 987654321?
tso

Posts: 798
Joined: 22 June 2005

I would surely like to know the "inventor" of this sequence "381654729".

Now seriously, I think we should have the common agreement that Euler didn't invent/contribute to the invention of this puzzle called sudoku, or even a square with N symbols (N=#cells in a row) each appearing N times without any symbol duplication in each row/column (i.e. the "Latin square"). He simply studied and researched about the latter concept.

Other than that, each person has the freedom to associate Euler to sudoku for any personal reasons. For example, if an undergraduate in MIT wants to write a thesis about sudoku and cite an Euler paper as one of the references, it's legitimate to do that. Or anybody in this forum can post a message that s/he got hooked to sudoku after reading an article about Euler and got interested in the Latin squares, and after googling the term "Latin squares" somehow discovered about sudoku grids... I think that's the "connection" dukuso means that we should not totally forbid.

The fact that a thread titled "Leonhard Euler" exists in this forum is proof that there is a "connection" between this dead mathematican called Euler and this popular puzzle called sudoku. In the same sense that George W. Bush has a "connection" with this bloke named Osama bin Laden... Perhaps "association" is a better word?
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:I would surely like to know the "inventor" of this sequence "381654729".

Although he/she would not have "invented" the sequence, someone must have been the first to actually think about this exact sequence of exactly nine digits. Who knows, it might have been the person who invented the following puzzle:
Find an integer which in decimal form is ABCDEFGHI, using only the digits 1 through 9, such that 1 divides A, 2 divides AB, 3 divides ABC, 4 divides ABCD, ..., 8 divides ABCDEFGH, and 9 divides ABCDEFGHI (treating each string as an integer in decimal representation). The only solution is ABCDEFGHI = 381654729.
r.e.s.

Posts: 337
Joined: 31 August 2005

That's a good one -- never saw it before. I'm going to intentionally forget that number and then try to solve the puzzle.

Digressing (regressing?) -- here's another Sudoku site that seems to make the ridiculous claim that Euler invented Magic Squares as well:

http://www.sudokuprime.com/default.aspx?id=10

I might not have pointed out this error, except that the page goes on to say: "If you want to learn more on Euler, the history of mathematics or the latin squares, we advise the reading of the following excellent books." Though we haven't bothered ourselves.
tso

Posts: 798
Joined: 22 June 2005

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