6670903752021072936960 is old hat

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6670903752021072936960 is old hat

Postby Red Ed » Fri Feb 01, 2008 11:18 pm

For the historians out there ...

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

:shock:
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Postby coloin » Sat Feb 02, 2008 1:42 am

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
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Postby Red Ed » Sat Feb 02, 2008 11:45 am

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.
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Postby coloin » Sat Feb 02, 2008 12:29 pm

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

If qscgz is reading this....

I say "well done"

C
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Postby gsf » Sat Feb 02, 2008 1:22 pm

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
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Postby coloin » Sat Feb 02, 2008 1:33 pm

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
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Postby Red Ed » Sat Feb 02, 2008 3:21 pm

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.
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Postby gsf » Sat Feb 02, 2008 6:00 pm

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?
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Postby coloin » Sat Feb 02, 2008 8:10 pm

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
:idea:[No]

C
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Postby Red Ed » Sat Feb 02, 2008 8:22 pm

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.
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Postby tinfoil » Sat Feb 09, 2008 10:02 pm

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.
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Postby Red Ed » Sun Feb 10, 2008 4:33 pm

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?)
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Postby tinfoil » Wed Feb 13, 2008 1:05 am

qscgz had been a frequent poster to that group

http://groups.google.co.uk/groups/profile?enc_user=v3J5DA0AAABJAeVSEMz5yobZxj2WYC9e

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!?
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Postby coloin » Wed Feb 13, 2008 6:26 pm

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. :roll:

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dukuso

C
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