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After solving a 9x9 Sudoku puzzle on paper, can you know if you have done it right without checking the whole answer grid, but only a set of columns, rows and/ or 3x3 squares? If yes, what is the minimum number of rows or colums or 3x3 squares, and which ones, that you need to check to know if your solution is right?

- Vaibhav
**Posts:**1**Joined:**15 September 2005

[quote="Vaibhav"]After solving a 9x9 Sudoku puzzle on paper, can you know if you have done it right without checking the whole answer grid..."

No! The puzzle grid contains 81 cells , any one of which could have an incorrect number in any cell. For a correctly completed puzzle, the summation of the nine numbers in each row, column and box (there are nine 3x3 boxes within the grid) must equal 45. However, each row, column and box should be checked individually to ensure no numbers are duplicated.

Regards Bonsai Cec

No! The puzzle grid contains 81 cells , any one of which could have an incorrect number in any cell. For a correctly completed puzzle, the summation of the nine numbers in each row, column and box (there are nine 3x3 boxes within the grid) must equal 45. However, each row, column and box should be checked individually to ensure no numbers are duplicated.

Regards Bonsai Cec

- Cec
**Posts:**1039**Joined:**16 June 2005

Max Beran wrote:Is that true - aren't any two of the three units sufficient to fix the third?

According to Pappocom there are 27 "units" in the puzzle grid - nine rows, nine columns and nine boxes. Not sure what you mean in checking two of the three units.

An error would be detected earlier if it occurs in row1 (or column 1) which presumably is the preferred starting checkpoint rather than checking other rows first. As I see it, the following shows why virtually checking the whole puzzle could be necessary:

If an error occurred in say box 9 which could show all digits 1 to 9 but not necessarily in their correct cell, this error would not be evident even if:

(a) the remaining eight boxes were correct

(b) the top and middle bands (boxes 1 to 6) were correct and

(c) the left and middle stacks (boxes 1,2,4,5,7 & 8) were correct.

The error would only become apparent after checking either rows 7,8 and 9 - which may still not reveal the error - or finally checking columns 7,8 & 9 to reveal the error.

I still can't see any "short cuts" to checking a puzzle solution which Vaibhav has asked other than restricting checking solely to rows and columns.

Bonsai Cec

- Cec
**Posts:**1039**Joined:**16 June 2005

Can someone give me an example of an invalid sudoku which can´t be identified by checking all rows and colums but only 8 blocks? I´m just curios…

- catilina
**Posts:**3**Joined:**25 August 2005

catilina wrote:Can someone give me an example of an invalid sudoku which can´t be identified by checking all rows and colums but only 8 blocks? I´m just curios…

Try swapping all cells in columns 3 & 4 or 6 & 7.

- angusj
**Posts:**306**Joined:**12 June 2005

catilina wrote "Can someone give me an example of an invalid sudoku which can´t be identified by checking all rows and colums but only 8 blocks? I´m just curios…"

Angusj wrote "Try swapping all cells in columns 3 & 4 or 6 & 7"

Following Angusj's above suggestion, I can now see that merely checking all rows and columns is not sufficient to confirm a correctly solved puzzle as I previously thought - hence the need to also check boxes. As usual, Angusj's comments are spot on.

Bonsai Cec

Angusj wrote "Try swapping all cells in columns 3 & 4 or 6 & 7"

Following Angusj's above suggestion, I can now see that merely checking all rows and columns is not sufficient to confirm a correctly solved puzzle as I previously thought - hence the need to also check boxes. As usual, Angusj's comments are spot on.

Bonsai Cec

- Cec
**Posts:**1039**Joined:**16 June 2005

angusj wrote:Try swapping all cells in columns 3 & 4 or 6 & 7.

angusj, I´m not convinced. Swapping 2 columns of different stacks does - normally - invalidate the adjacent boxes.

So again the question: I failed to actually construct an invalid sudoku that can´t identified by checking all rows and columns and 8 out of all 9 boxes. Is it possible? Or, otoh, is checking 26 (or 25,…(?)) "units" sufficient for a valid sudoku?

Btw, doesn´t swapping 2 columns imply not that the solution is wrong but the given clues, because at least one has to be in those 2 columns for a unique solution. Hope this makes sense

- catilina
**Posts:**3**Joined:**25 August 2005

catilina wrote:So again the question: I failed to actually construct an invalid sudoku that can´t identified by checking all rows and columns and 8 out of all 9 boxes. Is it possible?

Sorry, I misread your original question.

No, I don't know if checking just 7 or 8 boxes is sufficient once rows and columns have been checked.

- angusj
**Posts:**306**Joined:**12 June 2005

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