## Techniques for fast solving

Advanced methods and approaches for solving Sudoku puzzles

### Techniques for fast solving

What techniques do you use for fast solving? Do you scan the whole grid to find clues by random order, or maybe it is better to go in order - rows, columns, boxes or maybe scanning the 1's then the 2's, etc.?

I feel that up to medium level it is better to go by random order. In those levels, you can miss some clues and still get the solution.

In Hard level and up, I prefer to go by order. Otherwise, if you miss a clue, you might spend a lot of time to find it, as it might be the only possible next step.

I go by numbers - 1,2,3... for each digit, I look on its givens and placxe it where the givens limit it to only one place in a box. If there are two options, I mark it by pencil.

This stage may be done pretty quickly with some practice and significantly limits the candidates for the remaining cells.

Then, I put the candidates pancilmarks, starting with rows/columns/boxes that have low number of empty squares. For those empty squares, the pencilmarking is quicker and there is higher chance to find single candidates, double pairs, etc.

amnonj

Posts: 2
Joined: 18 August 2005

I use a slightly different technique to eliminate candidates, I look for what cannot be in a cell, e.g.

| * * * | * 8 4 | 3 * * |
| 8 * * | 6 * * | * 9 * |
| * 5 6 | * * 9 | 8 1 * |
--------------------------
| * 1 * | 2 4 * | * * 8 |
| * * 9 | * * * | 5 2 3 |
| 2 * 8 | * * 3 | * 4 * |
--------------------------
| * 8 * | 9 * * | 4 3 * |
| * 2 * | * * 1 | * * 7 |
| * * 7 | 4 6 * | * * * |

If you look att box (2,3) nr 9 is a candidate for r4c7, r6c7 and r6c9.
But nr 9 cannot be in r4c1, r4c3 and r4c6 therefore it ha tos be in r4c7.

So far I've never had to use thechniques with quads, triples, x-wings and stuff like that.

Cheers.
King Voodoo

Posts: 7
Joined: 05 July 2005

King Voodoo wrote:So far I've never had to use the techniques with quads, triples, x-wings and stuff like that.

If you've never used triples, which puzzles are you doing? Even when you use advanced tactics, you can't avoid using triples in most sudokus from Times difficult/Pappocom moderate and above.

G
george-no1

Posts: 150
Joined: 20 May 2005

Haven't tried those, can you giv me a link and i will try.

Thanks
King Voodoo

Posts: 7
Joined: 05 July 2005

I tend to look around the grid essentially at random (ar, as I like to call it, "stochastic"). I suppose there's some method to it, looking for the numbers that there are two of in a chute and seeing if you can place the third, and whatnot. And then if a pair jumps out at me, I try to deal with it straight away, avoiding pencilmerks if I possibly can, to speed the thing up. I suppose there's a limit to how diffiult puzzles can be and still be solved like this, but it works well enough for ones in newspapers.
PaulIQ164

Posts: 533
Joined: 16 July 2005

Try yesterday's Fiendish from The Times:

l.3.l...l.8.l
l..1l4.8l9..l
l.2.l.6.l.7.l
------------
l..3l.9.l8..l
l...l8.1l...l
l..5l.2.l6..l
------------
l.5.l.4.l.6.l
l..4l5.9l7..l
l.7.l...l.1.l

G
george-no1

Posts: 150
Joined: 20 May 2005

### My technique

This is how i do hard and worse sudokus
==================================

Basically there are 2 main stages in my solving teqnique:
==============================================
1) Solve as much as possible of the sudoku, without writing down all candidates. Write down multiple candidates selectively during this process...

The main Idea is to find a process where you scan the most promising information first. And scan the same information as few times as possible, writing down the information at the right time, without cluttering the board unnecessarilly.

2) Sudoku partially solved, non-fixed squares have all candidates written in the square. Squares with only 2 candidates have a pencilled square around the pair. (Simplifies spotting forcing chains).

Terminology:
HOUSE: box or row or column

1)
===
Go by numbers.

When finished with that number, write it down on the side. Take
the next number that has not been written down that seems most promising.

For each number, check for givens, apply as advanced logic as you want, given the information on the board. When done, make a judgement if you want to write down all remaining candidates for this number (the whole board). If they are few, write them down in the squares. Check for nishio, x-wing, etc. If the candidates are many, don't write them down yet.

=================
* Was the number too hard? then do NOT write it down on the side.
* Did you make progress, but did not write down the remaining candidates? Write down the number on the side, WITHOUT circling it.
* Did you write down all remaining candidates? (For the whole board)
Then write down the number on the side WITH a circle around it.

Take a new number, that has not been written down on the side.

Repeat until all numbers have been written down on the side.

During your progress, if you can prove that a cell only has 2 candidates,
draw a square around those candidates.

*BREATHER*
You will now have a list to on the side with numbers 1-9, some circeled, some not. The numbers with circles have all their possible candidates written in the cells of the board.

If you have more than 3 uncircelled numbers, reduce that number to 3.
All numbers, except these 3 should now have their candidates written on the board. These 3 numbers will be called a,b & c

Check for empty squares.
If yo have done things right up to now, empty squares can only hold (a,b, or c)
For each empty square, test for a,b&c. Chances are good that you quickly will find a few doubles. (ab, ac, or bc) Square these.

Complete each box.
=================
For each box, fill in candidates for a,b & c. (Don't check your squared doubles. You have already proven that they are complete. That's why you squared them) When a box is done, mark it
by pencilling the upper left edge.

You can also complete the box earlier if feasible. Remember to
pencil-mark the box only if all caldidates for all numbers have been checked in that box.

Remember to only circle a number on the side if candidates for that number have been written down for ALL boxes.

Step 1 DONE.
All candidates have now been filled in. During the whole process. Focus on recognizing nishio's and forcing chains. The fact that the bulk of the work is done number by number, makes it easier to recognise nisho and other number-specific patterns at an early stage.

2) Here you're on your own
Hopefully you have already cracked a nishio, forcing chain, or fishy cycle before you get here.

=============
Spotting hidden pairs: If number x and y populate the same 2 squares, and no other squares in a house, then these are a pair. You may happen spot this early before other candidates have been written down in the house.

Spotting x-wings and other number-specific patterns.
Since the bulk of the candidate entry is done per number not per house, the mind easier recognizes these patterns.

Variations:
=========
Write down candidates in only a few boxes. Good if you spot a box-row intersection that leads to reductions in a certain box, and you want to remember that, but the candidates for that number are too many in the other boxes. Remember to NOT circle the number on the side.

=============
Squaring double candidates sometimes causes me to miss them when
I am scanning rows and columns. This is because I initially wirte the candidates small in their respective position within the cell (divide the cell in a 3x3 grid), but if find a pair, I erase the small numbers and write the pair larger in the middle of the cell (with a square around)

That's my technique.

EDIT:
I can add that I break this process anytime when I find something useful that is wirth pursuing right away. This is no problem. My pencil-marked-boxes and numbers-on-the-side still apply and tells me where to continue when I get stuck again...
Last edited by govert on Fri Aug 19, 2005 12:15 pm, edited 1 time in total.
govert

Posts: 3
Joined: 19 August 2005

Heck.
PaulIQ164

Posts: 533
Joined: 16 July 2005

King Voodoo wrote:Haven't tried those, can you giv me a link and i will try.

Thanks

I'll give you a link to somewhere else:
http://www.menneske.no/sudoku/

Yes. The site is Norwegan, but there is a H*LL of a lot of sudokus, with different degrees of difficulty.

The "Villkårlig" menu will give you random sudokus with difficulty of your choice:
"Super lett" - Super Easy
"Veldig Lett" - Very Easy
"lett" - *guess*
"Medium" - *guess again*
"Vanskelig" - Hard
"Vanskeligere" - Harder
"Veldig Vanskelig" - *left as an exercise for the reader*
"Super Vanskelig" - ...

"Super Vanskelig" can sometimes only be solved by Trevor's Tables.
"Veldig Vanskelig" requires nishio / swordfish or similar techniques.

Have fun! I do
govert

Posts: 3
Joined: 19 August 2005

I am quite the amateur, but have found that I'm pretty fast with the easy to moderate level games in most papers (concentrate mostly on difficult ones at this point) with only pencil and paper.

Start by going through the numbers. With the first digit, I see how many boxrows and boxcolumns are already filled in (set of three linearly contiguous boxes with more than one 1 already filled in), and if there are any "intersections" (I picture a box without the digit as "shaded out" in rows or columns that already have that number in it). If the reduction yields to a placement, I write it in, of course. If it does not, I memorize the area.

Repeat for remaining 8 digits. During process, see if any of the shaded areas "cancel out" each other.
Dusty Chalk

Posts: 21
Joined: 15 August 2005

george-no1 wrote:you can't avoid using triples in most sudokus from Times difficult/Pappocom moderate and above.

????

- Wayne
Pappocom

Posts: 599
Joined: 05 March 2005

Pappocom wrote:
george-no1 wrote:you can't avoid using triples in most sudokus from Times difficult/Pappocom moderate and above.

????

- Wayne

Indeed Wayne - a surprise to me aswell. I suppose that if you want to find triples and do it that way then all fine and dandy - but there are much less painful ways! - unless of course you're experimenting to see how far a tactic will get you (as I did with x-wings the other day).

stuartn
stuartn

Posts: 211
Joined: 18 June 2005

All I meant was that in pretty much every Pappocom puzzles I do (i.e. Times difficult and fiendish) I find (naked or otherwise) triples, which help me to solve the puzzle. I wasn't trying to make a big announcement when I said that, I supposed I just assumed that everyone else used the triples as much as I did.

G
george-no1

Posts: 150
Joined: 20 May 2005

[quote]
"george-no1" Try yesterday's Fiendish from The Times:

l.3.l...l.8.l
l..1l4.8l9..l
l.2.l.6.l.7.l
------------
l..3l.9.l8..l
l...l8.1l...l
l..5l.2.l6..l
------------
l.5.l.4.l.6.l
l..4l5.9l7..l
l.7.l...l.1.l

G [/quote]

Tried it and i didn't have to use any triples
King Voodoo

Posts: 7
Joined: 05 July 2005

I use triples often, X-wings sometimes, for the puzzles in the Wash Post. It interests me to learn they are not, or at least not usually, needed. Perhaps I'm overlooking some simpler tactics, though I find these easy enough, fun to locate, and don't (yet) need anything more. BTW, I solve strictly via pencil and paper, though with heavy pencilmarks when stalled.
Doyle

Posts: 61
Joined: 11 July 2005

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