## 6670903752021072936960 is old hat

Everything about Sudoku that doesn't fit in one of the other sections

### 6670903752021072936960 is old hat

For the historians out there ...

Bertram and Frazer weren't the first! The honour goes to "qscgz", some 20 months earlier.

:shock:
Red Ed

Posts: 633
Joined: 06 June 2005

Ha

I did wonder if the number had been calculated before.......maybe in another galaxy

Is it likely that someone can come up with that number in 7 weeks on their own.....qscgz shows remarkable understanding and was able to program a computation.

This was before sudoku had hit the newspapers.

I think it might be more likely to be a hacker....except it isnt.

The previous posts from qscgz do imply a degree of ability [understatement]

Perhaps we could try qs...@aol.com

Respect

C
coloin

Posts: 1738
Joined: 05 May 2005

Not 7 weeks ... more like 5 years. He(?) posted on the same subject back in 1998, at which time he just did some Monte Carlo trials. Search for "rcc9s" on Google Groups.
Red Ed

Posts: 633
Joined: 06 June 2005

qscgz wrote:I found 46656 solutions ("rcc9s") , to place 9 queens
(or whatever) into a 9x9 square , such that no two queens are in
the same row,column or cell.

Two such rcc9s are called disjoint , if all their 18 queens are
on different squares.

A solved NPP (number place puzzle) is nothing but a set of 9 mutually
disjoint rcc9s.

Now I wrote a program that tried to generate solved NPPs in 9 steps:
On each step s :
count the number n(s) of rcc9s that are disjoint to all the other
previously selected rcc9s ,
and select one of those disjoint rcc9s at random.

some typical outcomes for the n(s) were:

46656,17972,6121,1848,443,96,24,2,1
46656,17972,6200,1716,470,81,10,0,-
46656,17972,6121,1848,443,96,24,2,1
46656,17972,6190,1879,426,96,18,4,1
46656,17972,6021,1784,359,63,4,0,-
46656,17972,6022,1688,383,82,10,0,-
46656,17972,6046,1748,420,82,11,0,-
46656,17972,6096,1680,392,88,14,2,1
46656,17972,6021,1712,306,72,14,0,-
46656,17972,6254,1942,528,122,11,0,-

Now I multiplied the n(s) , divided by 9! since the order doesn't
matter and got 1.5*10^16 in average.

qscgz

Yes this was in 1998 , "rcc9s" = "templates", and he certainly understood.

And this is a "Monte Carlo" estimation of 6670903752021072936960

Maybe this was refered to indirectly in the early days.... by Josh

I say "well done"

C
coloin

Posts: 1738
Joined: 05 May 2005

Red Ed wrote:Not 7 weeks ... more like 5 years. He(?) posted on the same subject back in 1998, at which time he just did some Monte Carlo trials. Search for "rcc9s" on Google Groups.

sep 1998 also provided an estimate on min #clues
qscgz wrote:My estimate for the number of different solved number-place-puzzles
is ~ 10^16 (found numerically,Monte Carlo).
So, if every clue reduces the number of solutions by a factor of 9 ,
then at least 17 clues would be necessary . ( 9^17 ~ 10^16)

I know I've groused on players/programmers forum posters to search twice post once
shame on me
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

I dont know how valid that estimation is !!

Sholdnt the big number be 6*10^21....?

Initilally the first clues reduce by a factor of 9, but the later clues do considerably more.

C
coloin

Posts: 1738
Joined: 05 May 2005

The big number in qscgz's post is an estimate of 6.67e21 / 9! - i.e. where symbol labelling is considered irrelevant.

I agree that his(?) methodology is off for estimating the number of clues. No points for qscgz on that count, in my book.
Red Ed

Posts: 633
Joined: 06 June 2005

Red Ed wrote:I agree that his(?) methodology is off for estimating the number of clues. No points for qscgz on that count, in my book.

points for intuition though
at that time I think the lowest known were ~20 clues
early forum guesses in 2005 were 19 and 18

and with the monte carlo wouldn't any estimates be based on some form of uniformity of data from start to finish?
assuming uniformity from the first digit templates to the last, leading to 17,
must be something of merit there, no?
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

Well, Im sure he [?] didnt do the Monte Carlo and the subsequent enumeration without making a few false assumptions along the way.
Code: Select all
`+---+---+---+|.2.|.7.|5..||4.6|...|...||.89|...|...|+---+---+---+|...|2.9|...||3..|...|1..||...|8..|...|+---+---+---+|5..|1..|...||...|...|.98||...|.4.|...|+---+---+---++---+---+---+|123|.7.|5..||456|...|...||789|...|...|+---+---+---+|...|2.9|...||3..|...|1..||...|8..|...|+---+---+---+|5..|1..|...||...|...|.98||...|.4.|...|+---+---+---+`

with reductions of 9! by fixing B1 it is possible to solve with 12 clues

Can we make this fit with the 10^16 number
[No]

C
coloin

Posts: 1738
Joined: 05 May 2005

The Monte Carlo bit was just there to estimate the 6.67e21 number. To get from there to "at least 17 clues" took a clumsy estimate which IMHO hit on 17 as the answer more by luck than by judgement. Qscgz seemed to retract it shortly afterwards ("I'm no longer glad with this").

I know I'm being a bit harsh.
Red Ed

Posts: 633
Joined: 06 June 2005

Back when Bertram and Frazer first posted their results in this thread, I Googled for 6670903752021072936960 and 6.67*10^21 and all the other ways to represent that number that I could think of, to see if they were the first (I also looked for the versions of 6.65E21 of MY estimate to see if I was the first).

At that time, I found nothing. Now this turns up. It is very strange.
tinfoil

Posts: 16
Joined: 06 June 2005

Odd, but not suspicious I think: it was a newsgroup posting that requires a special Google Groups search. I suppose we all just forgot to do that.

I will continue to think of B+F as the "fathers" of this result as it wasn't until their work that the calculation -- and thus any reason for believing the result -- was described. Qscgz's was just a number out of thin air: he was the first to claim the answer, but not (that I know of) first to prove it.

If you remain in doubt, why not email him/her. (Has anyone done that yet?)
Red Ed

Posts: 633
Joined: 06 June 2005

qscgz had been a frequent poster to that group

in the 'distant past', but after April 2002, he/she did not post for 17 months, including waiting 6 months after their quoted post, posted this SINGLE post with an unsubstantiated 'magic number' exactly matching B&F's 'later' number of 2005, and then never posted again! Doesn't this seem odd!?
tinfoil

Posts: 16
Joined: 06 June 2005

I dont think there is doubt that he [?] calculated the number when he did.
Red Ed wrote:Qscgz's was just a number out of thin air

Well....A 22 figure number cant really be coincidence.......

Perhaps an analogy approaching it is that he found it in the "thin air"somewhere near the summit of K2 [without oxygen and in his underpants, of course]

It looks as if he did the "Monte Carlo" estimation in 1998, see above, and then he produced the number with insight into the isomorphs/essentially different grids in September 2003.

There are many many other posts from this chap - so I cant believe it was hacked.

He also had the aptitude to solve "problems" with computor technigues especially latin squares and knights moves.

This chap also doesnt appear to want /need credit or recognition.

His alias does appear to have Gone from the Search engines however.

Hidden Text: Show
dukuso

dukuso wrote:
ahh yes, that's me.

I spent two weeks on that problem in 2002 or 2003 with a 500MHz computer,
all sorts of complicated pre-calculations.
Now they can do it in a fraction of a second !

I became interested in sudokus in 1999, the problems looked interesting to me,
I couldn't understand why it got so little attention ... until 2005

I'm not using the qscgz account very often - much spam, but you can still rech me there.
Be patient for a reply ...

I even got mentioned as qscgz in a paper from Brendan Mc.Kay.

best, Guenter

C
coloin

Posts: 1738
Joined: 05 May 2005