The New Sudoku Players' Forum

[stephenbuffalo]

What's the logic I have to use to get the next number? Not sure if I understand UR.


*-----------------------*
| 1 2 9| . . 7/ 6 8 .|
| 5 4 8| 9 2 6| 7 3 1|
| 7 3 6| 1 8 . | 2 . . |
|-------+-------+-------|
| 6 7 4| 8 . 1 | 9 2 . |
| 2 8 1 | . 9 . | . 6 7 |
| 9 5 3| 7 6 2| 4 1 8 |
|-------+-------+-------|
| 8 12| . 4 9 | . 7 6 |
| 3 9 5| 6 7 8 | 1 4 2|
| 4 6 7| 2 1 .| 8 . . |
*-----------------------*

[Carcul]

Hi Stephenbuffalo.

I have 3 solutions for you, in order of increasing difficulty (regarding the level of the logic involved):

1. Use colors on "3".

2. Use the Almost Unique Rectangle in cells r39c89 to set r3c9=4.

3. Use the Almost Deadly Turbot Fish in cells {r5c6|r5c7|r7c7|r7c4|r9c6} to set r5c6=4.

However, regarding the difficulty of finding, solution 3 is by far the easiest one (and also the one I preffer).

Carcul

[stephenbuffalo]

Hi Stephenbuffalo.

I have 3 solutions for you, in order of increasing difficulty (regarding the level of the logic involved):

1. Use colors on "3".

2. Use the Almost Unique Rectangle in cells r39c89 to set r3c9=4.

3. Use the Almost Deadly Turbot Fish in cells {r5c6|r5c7|r7c7|r7c4|r9c6} to set r5c6=4.

However, regarding the difficulty of finding, solution 3 is by far the easiest one (and also the one I preffer).

Carcul

Thanks, but where can I find how to apply these technique's. I seem to be entering a new world with different language.

[Sped]

Code: Select all

 
 *--------------------------------------------------*
 | 1    2    9    | 345A 35a  7    | 6    8    45   |
 | 5    4    8    | 9    2    6    | 7    3    1    |
 | 7    3    6    | 1    8    45   | 2    59   459  |
 |----------------+----------------+----------------|
 | 6    7    4    | 8    35A  1    | 9    2    35a  |
 | 2    8    1    | 345  9    345A | 35A  6    7    |
 | 9    5    3    | 7    6    2    | 4    1    8    |
 |----------------+----------------+----------------|
 | 8    1    2    | 35A  4    9    | 35a  7    6    |
 | 3    9    5    | 6    7    8    | 1    4    2    |
 | 4    6    7    | 2    1    35a  | 8    59   359A |
 *--------------------------------------------------*


"Coloring" is explained here:

http://angusj.com/sudoku/hints.php

Above, there are a lot of conjugate 3s. By conjugate it is meant that there are exactly two 3s in a group such that one of them must be true for 3 and the other false.

Look at row 1. There are two cells with 3s.. r1c4 and r1c5. One of them is true for 3 and the other false. I marked r1c4 "A" and r1c5 "a".

Column 5 has just two 3s, r1c5 is already a "a" so mark r4c5 "A". either all the "A" cells are 3 or all the "a" cells are 3.

Look at row 4. Just two 3s. r4c5 is already an "A", so mark r4c9 "a".

In column 9 there are just two 3s. r4c9 is already an "a", so mark r9c9 "A".

Row 9 has just two 3s. r9c9 is already an "A" so mark the other 3, r9c6 "a".

There are two 3s in column 6. r9c6 is already an "a" so mark r5c6 "A".

There are just two 3s in box 8. r9c6 is already an "a" so mark r7c4 "A".

Now, either all the "A" cells are 3 or all the "a" cells are 3. But look.. There are two "A" cells in column 4 (and in box 5 and row 5). Therefore the "A" cells cannot be 3s. The "a" cells must be 3s. So remove 3s from all the "A" cells and set all the "a" cells to 3.

Puzzle solved.

[Carcul]

Thanks, but where can I find how to apply these technique's.

See here and here.

[Cec]

"Coloring" is explained here:.........."

So clearly explained Sped.. I've saved it in my library.
Cec

[daj95376]

Now, either all the "A" cells are 3 or all the "a" cells are 3. But look.. There are two "A" cells in column 4 (and in box 5 and row 5). Therefore the "A" cells cannot be 3s. The "a" cells must be 3s. So remove 3s from all the "A" cells and set all the "a" cells to 3.

Puzzle solved.

Nice step-by-step explanation of Coloring. I just have one question. Why do you (and everyone else it seems) say 'remove 3s from all the "A" cells and set all the "a" cells to 3'? If you just set all of the "a" cells, then it'll take care of all the "A" cells.

[Sped]

Nice step-by-step explanation of Coloring. I just have one question. Why do you (and everyone else it seems) say 'remove 3s from all the "A" cells and set all the "a" cells to 3'? If you just set all of the "a" cells, then it'll take care of all the "A" cells.

It's not necessary to set the "a" cells to 3. With the 3s removed from the "A" cells, the "a" cells will all be hidden single 3s.

But I like to set them all at once, when they're still colored. It saves the trouble of finding them again.