## Carpet-bombing technique

Advanced methods and approaches for solving Sudoku puzzles

### Carpet-bombing technique

Hi all.
I've been doing the puzzle a couple of months now, and find it thoroughly enjoyable and addictive!

I guess its rather like doing crosswords....once the rules of the game are understood, it's easier to do, though of course having said that i appreciate that Sudoku is pure logic, whereas cryptic crosswords aren't.
.

For the first time last week i managed to complete both fiendish puzzles, much to my own surprise!

I've found a variance in the diffilculty levels of what are supposed to be the same level i.e moderate, hard etc.....or perhaps it's just that my brain isn't in gear that particular morning!

Ive seen some people say that they solve the puzzle by putting possible numbers in a cell....well i do also, but only to a maximum of two per cell, otherwise i get a blizzard of numbers and end up getting confused....i call that the "carpet-bombing" technique. One of the girls at work does it that way and it works for her so whatever suits i guess.

I have to admit occasionally i have to take a leap of faith to enter a number in a cell. Not very logical i know, but, again, it sometimes works.

It was heartening to see a letter from a University lecturer in Times 2 last week saying that nobody in her faculty (applied maths) had yet completed a fiendish puzzle.

I've no idea what applied maths is, but if she would like to give me a scholarship to go to her University and study it i would be delighted to attend!
chrisp

Posts: 1
Joined: 07 March 2005

### carpet bombing technique

Hi, I've used the carpet bombing technique to good effect. Having said that one needs to concentrate as it is easy to rub the wrong number out! When one has finished pencilling in the all the possibilities one is greeted with a veritable mass of numbers that it is easy to be blinded by!
Guest

### Just hard logic

Whilst woking on a solver I have found that most puzzels can be solved by just 2 aproaches, including the March competition one on this site.
Level 1 solver
For each empty cell draw the numbers 1..9. From this list the cross off the numbers in the row, col and sq. If you have a single number left that's an answer. When you put in an answer update the other lists for the row and col.
Repeat until finished or can make no more changes.
Level 2 solver
Using the updated lists from above go round each 3*3 sq and look in the lists for the empty cells to see what numbers are left.
eg ( 4,5 / 6,9 / 4,9 / 9,5 ) Each cell will have 2 or more numbers but over the 3*3 sq some numbers will only appear once. ( in this case 6 ) Those are your next answers.
Go back to level 1 solver and repeat.

You are stuck only when level 1 and level 2 solvers do not offer up a new answer. At that stage apply Level2 using col and row.

-- Gannett
Guest

### carpet bombing

i thought carpet bombing must do it. Get the obvious ones first then fill in the outstanding options -you thinkyou must have all the information to solve it.

But sometimes you have more info than you know and can eliminate some of the carpet bombing options.

Hard to explain but can be seen on some of the tips on this site.

Did today's with a combination of both but defy anyone to do it without putting in the 'carpet bomb' options

there's challenge Mr Gould
Guest

### Carpet Bombing - Alternative Representation

Hi, I use dot placement instead of listing all the numbers.

ie if a square has not been determined yet, but you know that you can exclude 1,2,5 then I put dots in the topleft, top middle, centre of the square.

an additional option is that, say 3,4 can be highlighted as possibilities by putting tiny circles in the top right, and middle left (I do this to highlight exclusive pairs). If the possibilities a ruled out later on, then the circles can be filled so that they become a dot (although a bit bigger than others).

Advantages of this method include space saving, dot pattern recognition.

Disadvantages are that a permanent ink pen makes dots the easiest, and that you have a higher chance of making a mistake by putting a dot in the wrong corner.

I also make a note of which numbers I've already determined 9 locations for (bad memory).

This graphical technique works with all the rules that I've seen listed.

Mark
Guest

### Carpet bombing

I agree with gmc, carpet bombing has started to tie me up in knots! One of the disadvantages I have found is a practical one: with so many numbers in a square there is a danger of rubbing out a number by mistake.
Guest

### Carpet bombing using dots -- some simple rules

Carpet bombing is the only technique I have ever used and it can be used to solve some so-called fiendish puzzles. The REAL fiendish ones are the ones where you have to do the "blind alley" technique (yuk)

Carpet bombing is done using dots to represent which numbers CAN'T occupy a given square. So no rubbing-out is required.
The position of the dot within a square indicates its number as follows :-

123
456
789

So, for example, if you have eliminated a "1" from occupying a square (because a "1" appears on the same row, column or box) then put a dot in the top left-hand corner or the square.
If a square contains these dots ...

Code: Select all
`oo  ooo o`

... it means that that square can not be 1,2,5,6,7 or 9

RULE 1: If a square contains 8 dots then that square must be the ninth number. Write it in and put the dots for that number in the unoccupied squares for that row, column and box.

E.g ...
Code: Select all
`oooooooo `

... means that the square must be a "3"

RULE 2: In a given row/column/box if only one square has a space for a number (ie all the other squares in the row/column/box have a dot for that number or already contain a number) then that square must be the ninth number. Write it in and put the dots for that number in the unoccupied squares for that row, column and box.

These 2 rules can be used to solve most puzzles - even fiendish ones.
There is a 3rd rule, but it is less often used.

RULE 3: In a row/column if the only squares that can contain a number are in the same box, then the other squares in that box can not contain that number. (So dot them)

Corollary: In a box if the only squares that can contain a number are in the same row or column, then the other squares in that row or column can not contain that number. (So dot them)
johnc

Posts: 2
Joined: 26 April 2005

Although this method will clearly solve any puzzle, it isn't particularly satisfying because it simply presents the user with the completed grid - it doesn't explain how the puzzle could have been solved in terms that the user could reasonably understand. A clear and concise explanation is an essential feature of a Sudoku solution.

On a more technical level, this carpet-bombing technique doesn't scale well - it slows horrendously if applied to a 4x4 Sudoku puzzle. I've found that for larger puzzles it's almost essential to incorporate some form of pattern-searching as discussed elsewhere on this forum.
Sue De Coq

Posts: 93
Joined: 01 April 2005

Sue De Coq wrote:Although this method will clearly solve any puzzle, it isn't particularly satisfying because it simply presents the user with the completed grid - it doesn't explain how the puzzle could have been solved in terms that the user could reasonably understand. A clear and concise explanation is an essential feature of a Sudoku solution.

It doesn't solve every puzzle.
It doesn't present the user with a completed grid.
You can only solve one square at a time.
The explanation of the solution will be a list such as
col 3 row 5 is "9" due to Rule 2(row)
col 9 row 1 is "5" due to Rule 2(box)
col 1 row 6 is "5" due to Rule 1
etc

You don't actually need the dots to apply the Rules, but it makes them much easier to spot
johnc

Posts: 2
Joined: 26 April 2005

Sue De Coq wrote:Although this method will clearly solve any puzzle, it isn't particularly satisfying because it simply presents the user with the completed grid - it doesn't explain how the puzzle could have been solved in terms that the user could reasonably understand. A clear and concise explanation is an essential feature of a Sudoku solution.

On a more technical level, this carpet-bombing technique doesn't scale well - it slows horrendously if applied to a 4x4 Sudoku puzzle. I've found that for larger puzzles it's almost essential to incorporate some form of pattern-searching as discussed elsewhere on this forum.
Guest

Posts: 312
Joined: 25 November 2005

### Re: carpet bombing technique

niko wrote:Hi, I've used the carpet bombing technique to good effect. Having said that one needs to concentrate as it is easy to rub the wrong number out! When one has finished pencilling in the all the possibilities one is greeted with a veritable mass of numbers that it is easy to be blinded by!

Before taking the "carpet bomb" approach, or the "dot-elimination" policy, it pays to fill in the obvious cells first. This will reduce the number of pencilled numbers (or increase the number of initial dots). Obvious cell filling follows the principle explained here.

Scan across the first three boxes in rows 1 2 and 3.
Look for solved cells that contain a value occurring twice. Look in the third box that does not contain that value. the missing value must be restricted to only 3 locations in the row not already occupied in the other two boxes.
If there is already a solution value in 2 of those cells, then the third cell is the only obvious location for that value. Write it in there.
If there is a solution value in just of those cells, then there are only 2 cells where that value can go. Check the columns for those 2 cells, to see if you can reduce the 2 cells to just 1. If so, again you can position that value. (you will be able to eliminate 1 of the 2 cells if the value occurs in the column of one of them).

Repeat this for the second, then third row of boxes, each time looking for two occurrences of a value.

Finally, do the above 3 steps for the 3 columns of boxes.

Once completed, you might even find it useful to check the rows again, given that you have filled in some cells that were not there originally.

Once you have done this 2 or 3 times, it becomes very easy. and you will find that there is less carpet to bomb.
Example

Code: Select all
`+ --- + --- + --- +| 6.. | 4.. | 821 || 7.. | .9. | ... || 2.4 | 8.6 | 7.. |+ --- + --- + --- +| ..5 | 6.7 | 3.8 || .7. | .3. | .6. || 3.6 | 2.1 | 9.. |+ --- + --- + --- +| ..7 | 9.4 | 1.2 || ... | .1. | ..3 || 198 | ..5 | ..6 |+ --- + --- + --- +`

In the top row of boxes, the values that occur twice are 2, 4, 6, 7 and 8.
Of these, 2, 7 and 8 can be placed immediately:
Code: Select all
`+ --- + --- + --- +| 6.. | 4.. | 821 || 78. | 792 | ... || 2.4 | 8.6 | 7.. |+ --- + --- + --- +| ..5 | 6.7 | 3.8 || .7. | .3. | .6. || 3.6 | 2.1 | 9.. |+ --- + --- + --- +| ..7 | 9.4 | 1.2 || ... | .1. | ..3 || 198 | ..5 | ..6 |+ --- + --- + --- + `

Next, look at 9 in the lowest row of boxes, before moving on to the columns of boxes . .

Terry (NZ)
Guest

### Re: carpet bombing technique

Terry NZ wrote:If there is a solution value in just of those cells, then there are only 2 cells where that value can go.

That should have been:
If there is a solution value in just one of those cells, then there are only 2 cells where that value can go.

Terry NZ
Guest

Hey everyone

Could someone tell me what the blind alley technique is

Help would be appreciated

Thanks
Darkozin
Darkozin

Posts: 11
Joined: 13 July 2006

Darkozin wrote:Could someone tell me what the blind alley technique is

blind alley <=> a mistaken, unproductive undertaking.

No offense intended but ... if you haven't yet monitored the Players' Forum for at least a couple of weeks, I suggest you do so before posting extensively.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA