## The technique I use to solve the puzzles

Advanced methods and approaches for solving Sudoku puzzles

### The technique I use to solve the puzzles

I have started doing medium and hard-level puzzles, and have come up with some methods of attack that help once the obvious bits have been solved. Here they are:

1. Mark each cell with all the values it could possibly take (tedious but necessary, and requires a the puzzle to be copied onto a suitably-sized piece of paper unless you are using the program)

2. Now examine each box, then row, then column and look for N cells that share the same N digits. When you find them, then all the other cells in the box or row or column may not use those digits.

For example, if in a row the possible solutions to 2 cells are both limited to 1 or 9, then no other cells in that row may have either 1 or 9 as a solution. These previously possible solutions may be struck out of those other cells , leaving the 2 cells with those 2 digits as allowed solutions.

Another example, if in a column 3 cells have the following possible solutions:
* 1 or 2
* 2 or 5
* 1 or 5
then no other cells in that column may have these 3 digits as possible solutions.

The 3 digits do not have to occur in pairs like that, they could also be arranged in 3 cells as
* 1 or 2
* 1 or 5
* 1 or 2 or 5

So you can see how the general principle arises from these examples.

3. If, in a box, a row, or a column, a cell uniquely holds a digit as a possible solution, then that is the solution for that cell.

For instance, after assigning all possible solutions to all the cells, you find that one cell alone in a row can accept 7 (apart from its other allowed solutions), then that cell must have 7 as its solution.

4. As a cell's value is determined, don't forget to visit all other cells in the same row, column and box to eliminate that digit from their possible solutions

5. As a cell's value is solved, don't forget to check if it immediately solves the value of other cells in the same row, column or box

6. Now repeat steps 2 to 5 until you are done.

Because I am sloppy, I find it useful - after assigning all possible solutions to each cell (step 1) - to go over them again and recheck. I usually find I have allowed to many solutions because I forgot to take a cell's box contents into account. Mistakes like that don't stop you getting to the end of the puzzle, but it slows things down until you catch and eliminate those excess solutions.

If you can't immediately see any step 3 type cells, then do the slow but methodical thing that I do for each box/row/column - go through each digit 1 to 9 and check if it has been solved, or if it is the possible solution to more than one cell in the (say) column. Your ruminations may go like this:

"1 - okay that is solved....2 - hmmm, that is a possible solution to more than one cell in the row I am checking, oh well....3 - errrm, wait a minute! This cell can take a number of solutions, but it is the only one in this row where 3 appears as a solution. Great, ignore its other possibilities, that cell's value must be 3 because no other cell in the row has 3 as a possible solution". And so on. A methodical approach is required with the techniques listed above, but they produce the results.

Using these techniques, there is no trial and error or what-if approaches required, just patient and accurate work. By this method I just solved a hard level puzzle in just under 31 minutes without any feedback from the program at all (i.e. the settings that allow you to get into the program's Hall of Fame).

I did originally put these notes on a blog I have just started up (http://ccx3.blogspot.com/), but I thought that this was a more useful place to put my notes.
ccx3

Posts: 5
Joined: 22 May 2005

### The technique I use to solve the puzzles

Yes, I worked out the same technique. However, I'm taking rather a long time to solve difficult puzzles, usually because I make a mistake - but the technique does work!
ArchieB

Posts: 9
Joined: 22 May 2005

I have found the same. I try and resist any tendency to rush, because that leads all to easily to missed solvable cells, and wrongly solved cells. If I find I have made some mistakes, but as long as the rot has not set in too far, I remove any suspect solved cells, re-examine suspect UNsolved cells to recheck that their solution candidates are still correct, then carry on. Works sometimes.

Periodically doing another sweep through all cells to recheck that they are still up-to-date with their solution candidates is good practice. It is so easy to suddenly find you have created a batch of definite solutions, rush through them writing in the solutions, and forget to update the surrounding cells (row/box/column) as you go.

If there are too many distractions, it may help to bind and gag the rest of the family, and the dog, until you have solved the puzzle. They'll understand and respect you for it.
Guest

Posts: 312
Joined: 25 November 2005

I did my first puzzle on Saturday night and worked out your method within the first hour - it seemed the only 'logical' solution!
Small problem though - I ruled up a special grid to give me extra room for pencilling possibles, then printed a few extra grids and did two more puzzles, then discovered it was 10 o'clock and I hadn't had dinner or fed the dog. Do I need this stimulation in my nice, well-ordered life?
Guest

where do u get most of your puzzles?
Guest

i got my first sudoku puzzles two days ago in a newspaper. i tried the V easy one on the first day for like 20 mins and got no where considering i didnt know any techniques. the next day i tried again and i picked up a few ideas so that WAS very easy, the easy one didnt take too long, medium a little longer and used a more advanced technique but i finished it. i only just finished the hard one using T&E and other new techniques, it took me almost all day, i was sick off school :P
Guest

Posts: 312
Joined: 25 November 2005

Guest

>> where do u get most of your puzzles?

I use the sudoku program which I bought after a month of using the trial version. I like the program because my scribbling on paper is so untidy. It is bad enough working through a puzzle without adding the extra burden of coping with my cramped and messy pencil notes!
ccx3

Posts: 5
Joined: 22 May 2005

### way of solving puzzles

this is my way of solving puzzles.............

i do not rush in to the problem.. i see the logic beyond it ...then i think in one shot.. then i try with t and e method.... 80% of the time i got the solution.. thank you

s vybhav
(student,rvce,bangalore)
s vybhav

Posts: 1
Joined: 23 May 2005

### Solving Techniques

Hi,

To speed up solving, I have an intermediate step to your starting off by filling in all candidates in all cells. I initially only "pencil" in candidates in 3x3 blocks where a candidate number can only occur twice (obviously if a candidate occurs once - it is the solution for that cell). This way it is easier and quicker to spot possibilities (e.g. if in a 3x3 block there are the same two cells with only the possibility of a 3 & 4 - say - then when I am subsequently filling in all possible candidates for that block, I immediately know that I can ignore other possible candidates for these two cells). Also by initially only pencilling in two candidates in each 3x3 block, I find it is easier to see certain eliminations. e.g.:-

if r1c1 candidates are 2,6
and r1c2 candidates are 2,3,6
and r1c3 candidate is 3

Then I can immediately see that I can eliminate the candidate 3 from r1c2 & that cell r1c3 must be a 3.

Hope you get the idea
Homer

Posts: 10
Joined: 20 June 2005