Advanced methods and approaches for solving Sudoku puzzles

I have recently become a sudoku fan, playing both games everyday. I do manage to finish both everytime although i'm sure my times will not win any competitions. My enjoyment however has been tarnished by the frustration of not being able to get started on the killer Sudoku challenges. It's very frustrating to read about people's increased enjoyment!

Everytime I try and start one I seem to come up against a huge amount of possibilities for the numbers. The Times' example explains that a 3 can use a 2 and 1 which is fair enough. But what about 7, it could use 6 and 1 or 5 and 2 or 4 and 3. Also, when the groups of numbers cross a table, this means numbers could be repeated so for a 9 in an L shape you could have 2 and 2 and 5 or 1 and 1 and 7 etc. I'm sure Im getting it wrong somewhere.

Could someone please explain in simpleton terms?
Yours gratefully, Mike
mpanter

Posts: 1
Joined: 07 September 2005

Right, I'll get through as many things as I can think of:

First, this should really be in the Times forum, but never mind.

Now, Killer sudokus. A simple trick to remember is that, since every row, column and box in a sudoku puzzle must contain 1 to 9, every row, column and box must logically add up to 45 (1+2+3+4+5+6+7+8+9). So, if you look at the Killer in today's times2, and look at the middle row,you'll see it consists of a bar of four cells adding up to 10, another adding up to 30, and one extra cell (the one in the very centre). Since the entire row must total 45, and the two bars of four together total 40, you know that the central cell must be a 5.

A controversial topic that you mention is the possibility of repeated numbers in an L-shaped enclosure. The Times have never specifically stated that this can't happen, though their stated rules sort of implied it. However, tso, who knows a great many things about stuff like this, assures us that it's an oversight on The Times' part, and it is in fact a rule that the no dotted enclosure can hold the same number twice. So, as an example, look at the top-middle box in today's puzzle (Box 2). There's a 2-cell enclosure that totals 3, so it must contain the 1 and the 2 in some order. Now look at the L-shape enclosure totalling 6 that just pokes its head into this box. The only way to make 6 is with 1+2+3. But you already have a 1 and a 2 in the top-middle box, so the part of the L that's in this box must be the 3.

One more example (yes, OK, now I'm just doing this for my own benefit). The very middle column has to total 45. You'ce got a big huge bar in the middle 7 cells that totals 35, so the cells at the top and bottom must add up to 10. The one at the top, as mentioned, must be a 1 or a 2. So the one at the bottom must be a 9 or an 8. But notice that it and the cell to the left of it have to add up to 16. If it were an 8, you'd need 8+8. And you can't have two 8s next to each other. So it must be a 9. That means next to it must be a 7, and you can place the 1 and the 2 in the 3-enclosure at the top.

Most importantly, once you have a few numbers in, don't forget to use the normal sudoku tehniques too!
PaulIQ164

Posts: 533
Joined: 16 July 2005

There is a solver here:

http://homepage3.nifty.com/funahashi/game/game676eng.html

I've tested it on two puzzles. It took only a 10 or 15 seconds to solve one I posted in another thread (http://forum.enjoysudoku.com/viewtopic.php?t=995&postdays=0&postorder=asc&start=0 but it took many minutes to solve the "Deadly" one here: http://www.timesonline.co.uk/article/0,,7-1757275_2,00.html

NOTE: This solver reported one and only one solution to the puzzle I posted previously, though that puzzle has two additional solutions if you ignore the "no duplicate digits in an enclosure" rule.
tso

Posts: 798
Joined: 22 June 2005

tso wrote:There is a solver here:

http://homepage3.nifty.com/funahashi/game/game676eng.html

I've tested it on two puzzles. It took only a 10 or 15 seconds to solve one I posted in another thread (http://forum.enjoysudoku.com/viewtopic.php?t=995&postdays=0&postorder=asc&start=0 but it took many minutes to solve the "Deadly" one here: http://www.timesonline.co.uk/article/0,,7-1757275_2,00.html

NOTE: This solver reported one and only one solution to the puzzle I posted previously, though that puzzle has two additional solutions if you ignore the "no duplicate digits in an enclosure" rule.

you can solve these as an exact cover problem generating all the
possible sums. You get a 11530*324 matrix.

The computer solves it with rather few nodes in only 4/18 seconds :
nodes:2 3 4 8 14 14 20 14 4 4 4 4 4 2 4 7 3 3 2 2 1 1 1 1 1 , 4 ticks
n=11530 m=324 Sr=24 Sc=5760

solver at
http://magictour.free.fr/killer.exe
source at:
http://www.setbb.com/phpbb/viewtopic.php?t=213&mforum=sudoku
dukuso

Posts: 479
Joined: 25 June 2005

mpanter wrote:I have recently become a sudoku fan, playing both games everyday. I do manage to finish both everytime although i'm sure my times will not win any competitions. My enjoyment however has been tarnished by the frustration of not being able to get started on the killer Sudoku challenges. It's very frustrating to read about people's increased enjoyment!

Everytime I try and start one I seem to come up against a huge amount of possibilities for the numbers. The Times' example explains that a 3 can use a 2 and 1 which is fair enough. But what about 7, it could use 6 and 1 or 5 and 2 or 4 and 3. Also, when the groups of numbers cross a table, this means numbers could be repeated so for a 9 in an L shape you could have 2 and 2 and 5 or 1 and 1 and 7 etc. I'm sure Im getting it wrong somewhere.

Could someone please explain in simpleton terms?
Yours gratefully, Mike
mbpatil369

Posts: 1
Joined: 11 September 2005

### killer

dukuso wrote:
tso wrote:There is a solver here:

http://homepage3.nifty.com/funahashi/game/game676eng.html

I've tested it on two puzzles. It took only a 10 or 15 seconds to solve one I posted in another thread (http://forum.enjoysudoku.com/viewtopic.php?t=995&postdays=0&postorder=asc&start=0 but it took many minutes to solve the "Deadly" one here: http://www.timesonline.co.uk/article/0,,7-1757275_2,00.html

NOTE: This solver reported one and only one solution to the puzzle I posted previously, though that puzzle has two additional solutions if you ignore the "no duplicate digits in an enclosure" rule.

you can solve these as an exact cover problem generating all the
possible sums. You get a 11530*324 matrix.

The computer solves it with rather few nodes in only 4/18 seconds :
nodes:2 3 4 8 14 14 20 14 4 4 4 4 4 2 4 7 3 3 2 2 1 1 1 1 1 , 4 ticks
n=11530 m=324 Sr=24 Sc=5760

solver at
http://magictour.free.fr/killer.exe
source at:
http://www.setbb.com/phpbb/viewtopic.php?t=213&mforum=sudoku

Errrrr... why?
stuartn

Posts: 211
Joined: 18 June 2005

A few days ago I wrote up a page of tips on solving these problems, with illustrated examples taken from the Times "Deadly" sudoku puzzle--it's available here:

http://www.ndorward.com/blog/?page_id=50

Doesn't say anything not already said above but the extra examples & lists of combinations may help.

Incidentally, I do find the Times' ratings & timings of puzzles very odd--the recent "Tricky" one I found a snap, completing it under the 20 minutes they set for it, whereas some of the supposedly easier ones caused me no end of grief. I've no idea how they calculate the difficult levels for the killer puzzles.....
nd

Posts: 28
Joined: 11 September 2005

### Killer Sudoku tips

I've posted a few Killer Sudoku solving tips at my site. There is also a calculator that helps you figure out all possible combinations of cells that add up to a given cage sum.

www.djape.net
djape

Posts: 34
Joined: 27 September 2005