For the historians out there ...
Bertram and Frazer weren't the first! The honour goes to "qscgz", some 20 months earlier.
:shock:
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
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.
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)
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.
+---+---+---+
|.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.|...|
+---+---+---+
Red Ed wrote:Qscgz's was just a number out of thin air
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