I've received a lot of interesting comments and questions from Sudoku fans over the last few years and this page
is where I try to answer them. Please feel free to drop me a note on the side of the page or try the Facebook
comment box. Or you can email me directly at firstname.lastname@example.org.
Post a Comment or Question here...
... by: Jonathan Norris, London, UK
Using your excellent Killer Solver, I'm still having difficulty in understanding Cage Splitting. The examples in the article are easy to understand, but the jargon used by the Solver is rather impenetrable... Blocks of... Many inside/outside, inside/outside value. I wonder whether you can find a way of getting the meaning across. It would be very grateful...
Andrew Stuart writes (16-Jun-2013):
Quite correct, the textual output is pretty obscure. I've just released a version which I hope improves this. For example, now says
Killer Cage Splitting
All the cages entirely inside columns 1,2 add up to 70. The cage starting on C1 can be split into an Innie (4 cells that sum to 20) and an Outie (2 cells that sum to 12). The new cages have combinations that mean...
we an remove 1/2/6 from A3
we an remove 1/2/6 from A4
... by: Flozoe11, Newport News, VA
I really like you website. My brothers got me hooked on Sudoku on our cruise and your site helped me become mor knowledgeable of how to solve and I like the fact that it's online. Better for me since I like being at my computer. Thanks so much.
Andrew Stuart writes (13-Jun-2013):
Hi, your very welcome! Thanks for the feedback
... by: Simon McCarthy, UK
First let me compliment you on an excellent website. I've often wondered how Sudoku puzzles are created and what the minimum number of clues to ensure a unique solution was - I haven't finished reading the proof of the latter, but I am finding it very interesting. Also, your killer Sudoku solver is a genius (and makes them all seem really easy, no matter how long I take using a pen and paper).
Anyway, I was curious to know whether you ever thought of an easy way to email and import Killer Sudoku? (It says on the notes that you wrote on your Killer Sudoku solver v1.02 that you were intending to come up with a method). I should point out, that I come from a mathematical background, rather than a programming one (so have some idea what this problem is about, but may not understand all of the intricacies).
Having said that, I reckon it must be possible to encode a Killer Sudoku (without using too long a string!) What's the maximum length the string is allowed to be? I reckon it's possible to describe any Killer Sudoku in any state of completion, using a string of 619 characters. Would that be too long?
Andrew Stuart writes (10-Jun-2013):
Killers require the cages and the clue numbers. The grid, the box shapes and the size is assumed. In the early days I noticed a lot of definitions tried to use cage boundaries but this is overly complex. For me, it is sufficient to have a 'mapping color' (the classic 4 color mapping problem) and a cage boundary is merely where adjacency has two different colors. The mapping color algorithm is most visible in the cage drawing popup (see "Enter New Killer") but it very basic - I allow a fifth color if necessary (A sixth is available but I've never seen it). Internally cages are numbered so I can uniquely identify them and create more (cage splitting strategy eg) and the numbering could be used instead of the mapping color but the mapping color only requires one digit.
Clues are assumed to be placed in the top leftmost cell of any cage. The solver will barf if they are not. This leaves a lot of zeros. A string of numbers delimited by commas would be shorter but harder to debug/read manually. So the 'standard' email link I employ is 81+162 characters of data:
Click on this link:http://www.sudokuwiki.org/killersudoku.htm?bd=1121222121221131321333231332314244442414122222
Now, there is huge scope for compressing this but I havenít researched it - something I've been meaning to do. I have noticed that some email systems refuse to turn this into a hyper link that includes all the data, which is annoying - and thatís the only reason I'd want to compress it.
I should also get on and do the import popup but I'm not sure how anyone else stores their killers electronically. Sudoku definitions abound (and are easy to import) but killer needs two different strings as input. I've assumed most people will be 'importing' through a link like the one above.
... by: Stephen Carman, retired Electronic Technician
Load Sudoku: CLICK TO LOAD
Every single time I try to eliminate candidates using a chain I seem to go wrong somewhere. The following board and chain is a perfect example. When I write my chain for this one solution puzzle the chain suggests exactly the opposite of what I know to be the correct candidate. Either I'm making a mistake in the interpretation of what the chain is telling me or I'm making a mistake in the chain itself. If anyone can explain where I'm going wrong I'd be less puzzled. :( Here is my chain followed by the board.
+2J8-8J8 +8H8-2H8 +2H3-5H3 +5j1 which is impossible given J4. If this chain is written correctly then how is it that I should interpret it's results? If it is written incorrectly then where did I go wrong?
| 3 16 9 | 256 18 258 | 4 7 25 |
| 2 146 15 | 7 134 9 | 8 16 35 |
| 145 8 7 | 2456 134 235 | 9 126 235 |
| 7 5 4 | 8 6 1 | 2 3 9 |
| 6 13 13 | 9 2 4 | 7 5 8 |
| 9 2 8 | 3 5 7 | 6 4 1 |
| 148 1347 123 | 24 3478 238 | 5 9 6 |
| 458 49 25 | 1 489 6 | 3 28 7 |
| 58 379 6 | 25 3789 2358 | 1 28 4 |
Andrew Stuart writes (13-Jun-2013):
Small mistake in your chain, easily done, but you are working with the correct idea.
In this case you can't turn off -5[h3] AND then ON +5[j1] because there is another 5 in H1. When you turn OFF and make a strong link there must be only two candidates left in the unit or cell. Weak links where you turn ON obliterates all other candidates in every direction from two upwards.
Hope that helps
... by: Robin Thornton, France
I have a problem concerning the Daily Killer for 23/5/2013
and I have spotted an error in your explanation for a step. However firstly I would like to complement you on your marvelous site and thank you for all the pleasure it has given me.
I was stuck in attempting to solve yesterday's Killer so I stepped through your solution and all went exactly according to my own progress until I reached the step in which you said that the 4's could be removed from A4 and A6 on the grounds that the valid combinations for a Cage of value 10 with 3 cells would not allow them. Here you gave the valid numbers adding up to 10 for a Cage of 3 cells in which you included 8 and 9 which are clearly not possible (the error). I cannot reproduce the puzzle so I can only refer to my own paper version. At this point I had possibles :-
As there is no 1 in B5 it would be perfectly possible to have:
A5 1 A5 4
A6 4 or A6 1
B5 5 B5 5
Hence no reason to remove the 4's from A5 and A6?
As your Solver managed to solve the Killer your action must have been correct but for the life of me I cannot understand your reasoning.
Keep up the good work!
Andrew Stuart writes (25-May-2013):
Very well observed and yes there was a bug in the output string. Took me all day to track down because a) the code is a few years old now in those parts and b) we are dealing with a cage that had been split, so the original 21 clue over 5 cells wasnít being used but the pseudo cage of 10 over 3 cells. What also throw me was the solver was splitting the cage even though there were no eliminations to be done - and then moving on to the next strategy, which is okay, since normally a split cage will make things easier. I have now added the word "split" to "cage" if it is a split cage.
I've also improved the text returned on cage combinations. I also spotted another bug where the last remaining cell in a cage wasn't being returned. A Bit of a howler that as itís an easy thing to compute and a human would fill it doing it on pen a and pencil. But it is now showing on the solver. The check was in my offline solver which is probably why I didn't spot it before.
Solvers all say version 1.94 now, so refresh a few times if you donít see that.
... by: Chris Williams, Fairford, UK
Easily the best killer solver available. Thank you, Andrew for making it available to us. A solver that just solves the puzzle is useless as we know it'll work; how is the question! This talks you through very nicely and has just got me through Times 3147 that had me stuck for days.
This isn't perfect yet and quite often runs out of ideas, but it's the best out there so well done!
Andrew Stuart writes (22-May-2013):
Cheers Chris, kind words thank you. Killer solver still lags behind Sudoku solver somewhat but I've been given some good hints by various people. I'll keep chipping away at it, you can be sure.
Share and enjoy
... by: Amy Hartner, U.S.A.
Thank you so much! A very evil sudoku plagued me for days until I came to this site and learned the X Wing Strategy. I look forward to using it in the future. I feel like a pro.
Andrew Stuart writes (16-May-2013):
Very glad the website is working for you, have fun!
... by: PeteTy, usa
was rather hard took me about 45 min by P&P
order of operations
5(2) cage with outie 4 next step...
Killer Hard Combinations
KILLER COMBO (Hard) on B7: cage of size 2 with clue of 5+ can only be 1/2/4/7/9, removing 3/5/6/8
just kind of wondering what easy combinations are
5(2) cage cant have 56789 which is probably a human ez step
a 2 cage with a 4 in one cell seems sort of obvious to me
also i was unchecking all the normal sudoku boxes i could
and noticed the check box for diabolical and extreme
preforms an xor with all the checked boxes
I assumed it would turn them all on or off
Andrew Stuart writes (30-Apr-2013):
I split the combinations strategy into two parts because one is much easier than another - in most cases. The 'easy' is where a cage has only one combination. From that it will be fairly obvious what candidates can be pruned. The 'hard' is where several combinations are possible and its more work to work out what can be removed just from the combinations. The solver does take into account what remains so easy and hard are not fixed. However, if you are half way through a puzzle lots of other eliminations may make a so-called hard relatively easy to work out, combination wise. I was thinking in terms of how a human would approach a puzzle and they, I assume, would want to pick off the easy combination cages first.
The XOR on the groups of strategies is by design but I can't remember why I did it like that : )
... by: Dale E. Kloss, Portland, Oregon, USA
I was working a Jigsaw Sudoku and it occurred to me to ask:
For a Jigsaw puzzle maker, how many unique puzzle shapes could be made?
Note that I'm asking about ONLY puzzle SHAPES not where each number goes.
Thanks. Dale Kloss
Andrew Stuart writes (30-Apr-2013):
I do not know, to be honest. Thatís a difficult combinatorics problem. For a jigsaw shape pattern to be 'nice' I prefer never to use cages that approximate a row or column, ie more than 7 cells in a line. That removes a large number. To still be Sudoku the shapes shouldn't map onto existing constraints. Reflection, rotation and other symmetries multiply the total number of 'unique' patterns.
... by: masonx, usa
This is great , I love to do these puzzles in the newspaper. I don't always have enough time before work and could use just a hint or two without screwing up the whole puzzle. If I have time I will do it alone. Thanks for sharing this , it works great.