Sudoku Puzzles

10:00 Good Maen!

16:33, but needed one carefully considered guess...

Very Funny! - Three days into Summer and we get a snowman. - Well it's something to look forward to.

Very appropriate! - Four days into the winter in Oz

Hurried through this one:

1) Start at 23 filled - the given puzzle. Unique Possibilities to 28. (UP 28).

2a) g6=9 == g9=9 -- g9=3 == g4=3 -- h45=3 == {h4=67,h5=46, h6=467} forbids g6=4 (depth 5)
2b) best as a matrix:
g1=1 g1=4
0000 i2=4 e2=4 d2=4
0000 0000 e2=2 0000 More...

25:40

Matrix explanation:
rows are 'strong sets' - at least one item each row is true.
Columns, except the first column - are 'weak sets' - at most one item in each column is true.
The matrix is 6 by 6, it has six truths minimum.
In columns 2 thru 6, there are at most 5 truths.
Therefor, More...

Good Maen to all! Seen that snowman before, and if he sticks around here today, he'll be a hat and scarf floating in a pool of water by nightfall!

1) Start 23, Unique Possibilities (UP) to 28.
2) g6=4 -- g8=4 == g8=8 -- g4=8, and g6=4 -- g1=4 == g1=1 -- g4=1, so g6=4 -- g4=18. Therefore, the chain g4=18 == g4=3 -- h45=3 == h456={triplet 467} forbids g6=4.
3) Hidden pair 47 at fh6 forbids f6=6, h6=6. UP 30.
4) Hidden pair 69 at c16 More...

New improved proof after seeing Steve's.

1) Start 23, Unique Possibilities (UP) to 28.
2) g6=9 == g9=9 -- g9=3 == g4=3 -- h45=3 == h456={triplet 467} forbids g16={pair 14}. Since g1=1 == g1=4, this forces g6<>14, so g6=9. UP 81.

Forget I posted that second proof. I can see the problem with it now.

I got it in just under 16 minutes but I thought it was a reasonably hard puzzle.

HI Steve, I am interested in seeing more detailed introduction to the matrices. Not sure what the 0's represent and how they are set up and then what to do with them. So I guess I really don't know anything about them at all. But I am interested in learning. Is there a site that explains them clearly?

Thanks.

Was this one easy too? Only needed one very good guess and my time was 5:38. First time to be under 6 minutes on a tough! I have had a few days over 7-8 minutes recently, so this was great.

The snowman is very nice. A lot of hard work went into it!

ten minutes exact..but struggled a bit,didnt flow easy..may be iam a bit out of touch..not done the tough for a couple of days.anyway finished to see the melting snow man(rather thats what canuk is predicting)
cheers

A nice one today:
1) UP to 28.
2) Triangular matrix
a5=9 i5=9 0000 0000 0000
a5=8 i5=8 b5=8 0000 0000
0000 0000 b5=3 h5=3 0000
0000 0000 0000 g4=3 g9=3
0000 g6=9 0000 0000 g9=9 forbids a5=2; UP to 31.
3) c79=58 forbids c126a89=58; UP to 35.
4) Pigeonhole (as well as More...

Andrei, same question as to Steve. Where do I find info on how to set up and use the matrices? What does the notation signify? Thanks.

19:24

Jill: the matrices work as follows. Each entry is some collection of possibilities (= candidates) (mostly, just one candidate, but could be more, and also could be empty, which is what 0000 stands for). In each row, at least one of the candidates must be true. There are two kinds of conditions on More...

Fantastic solution today andrei!
Your step 2 is especially brilliant.
If one wishes to, a minor improvement could be made on step 4:
g6=9 g9=9
0000 g9=3 g4=3
0000 0000 h4=3 h4=6
h5=4 0000 h5=3 h5=6
forbids g6=4.
If we combine andrei's proof with this minor adjustment: Rating drops to: .31+.03+.15=.49
Total sets: 11. max depth 5.

One could further improve proof/solution today --- slightly - very slightly - .... I will leave it to others to find it - hint: can reduce it by one set, same max depth, rating drops only to .47

8:44 with a reocrd 7 'gimmes' during setup! good mAen all.

oops: record

Steve, nice improvement!

Thanks Andrei! Should I post the complete improved proof? - so that it is all in one place - or should I leave it to those interested enough to wade through the posts?
BTW - I never came close to seeing the forbidding of the 2 at a5, although my instincts told me to look at the 2's - I just could not see the strong 8's in row 5 and how they worked against that 2.

Thanks. Working on it. Seems hard to do the setups. I tried to do some but once I got the 5x5 set up where the rows and columns all coordinated properly, the stuff in column 1 didn't seem to rule anything out. How do you decide where to start? And is there a sort of concrete theoretical proof or general discussion of this technique somewhere?

The pictures of me..... Major Brain Freeze

Jill, I have a draft of a joint paper with Bruno Greco on this stuff, that hopefully we will finish one day. The write-up contains complete proofs but is quite dense, with many examples yet not inserted in their proper places. If you wish me to email it to you, send me a message (Google me as More...

Complete improved combined proof posted in one place:
Step 2 is entirely Andrei's.
Step 3 is only an efficiency modification step for his Step 3, as it makes only a very minor change in number of sets used.
Step 4 is basically my original step 2a, adjusted for a solved cell - reducing More...

Hi all,
I am trying to develop a program to help with difficult Sudokus. At the moment, I have a program which works pretty well, finds singles, pairs, triples, gives a separate display of possibles for each number and has another separate display to help with forbidding chains.
Next plans More...

Oh, and the program was developed with Delphi 3 on Windows 2000, so it will be interesting for me to know if it even functions with XP etc.

I am only asking in this forum because it is the best one I know.

Very sad coment today after the match against my hubands team Argentina.
Been a player for quite some time, first time comment. Difficult one today, maybe it was the football.

29:50. Got it out after looking at Clark's proof. But I want to know how do you know where to start looking for these chains? What is the 'hint' you see or look for

hi every one

3:51. No guesses. Seemed quite easy.

14:02 and yes, it did seem like lots more easy fills before I had to start thinking than usual.

snowman is a repeat, we seem to have lost the tough gallery AGAIN, Gath!

Brrrrrrrr

3:51 ? Try to post it at 'Easy', good chance they'll believe you :)