The New Sudoku Players' Forum

[pingu]

hello guys I was wondering about an elimination of the number 9

Is there a move that eliminates this red 9 if yes explain me please

[SpAce]

Is there a move that eliminates this red 9 if yes explain me please

Yes, though I don't know why you would want to, as easier and more effective eliminations exist. Before addressing that in Part 2, I will answer your specific question anyway.

Part 1.

The simplest way to see if something can be eliminated is to assume it's true and see if it produces a contradiction. That's a basic trial and error (T&E) tactic, so it's not very elegant, but it works and is quite easy to understand even for beginners. Let's try it:

Assume r8c6=9 -> r9c6=4 -> r7c9=4 -> r3c9=5 -> r3c6=9: contradiction (two 9s in c6) => r8c6<>9

That's just one way to do it. No matter how you approach it, it will always produce a contradiction of some kind.

That can be seen and expressed more elegantly and effectively as an AIC loop:

Code: Select all

.------------------.---------------------.----------------------.
| 79   379    5    |  679   4     8      | 36     1      2      |
| 2    8      347  |  67    56    1      | 9      3456   56-4   |
| 49   6      1    |  3     2    a5[9]   | 8      7     b45     |
:------------------+---------------------+----------------------:
| 18   23479  6    |  5     19    247-9  | 2347   234    789-4  |
| 5    23479  3479 |  2469  8     2467-9 | 23467  2346   1      |
| 18   2479   479  |  2469  169   3      | 5      246    6789-4 |
:------------------+---------------------+----------------------:
| 3    5      8    | d24    7    d246    | 1      9     c46     |
| 479  479    2    |  1     569   56-49  | 467    8      3      |
| 6    1      479  |  8     3    e4(9)   | 247    245    57-4   |
'------------------'---------------------'----------------------'

(9=5)r3c6 - (5=4)r3c9 - r7c9 = r7c46 - (4=9)r9c6 - loop => -4 r2469c9, -4 r8c6, -9 r458c6

That chain proves that either r3c6 or r9c6 must be 9, so anything between them (including r8c6) can't be. Because the two end points also see each other, it's actually a loop, which gives us a bunch of other eliminations along the chain as well.

Anyway, I don't really understand why you would want to target a specific candidate like that, especially since it doesn't seem very helpful in solving the rest. So, let's look at what else you could do.

Part 2.

First of all, what did you use to eliminate 6 from r7c4? It's not hard, but it requires a non-basic technique. I'm just wondering why you'd do that before even completing all basics. Notice that you have a Hidden Pair (89) in r46c9. If you execute that, you'll get a few more placements and eliminations:

Hidden Pair (89) / Naked Triple (456) c9 => +7r9c9, +5r9c8, +2r9c7
Claiming (7)r6\b4: -7 b4p256
Naked Triple (189) / Hidden Quad (2347) r4: -9 r4c26

Those basics get us here (note that I returned the 6r7c4, because it wasn't a basic elimination or really useful):

Code: Select all

.----------------.------------------.-----------------.
| 79   379   5   | 679   4    8     | 36    1     2   |
| 2    8     347 | 67    56   1     | 9     346   456 |
| 49   6     1   | 3     2    59    | 8     7     45  |
:----------------+------------------+-----------------:
| 18   234   6   | 5     19   247   | 347   234   89  |
| 5    2349  349 | 2469  8    24679 | 3467  2346  1   |
| 18   2479  479 | 2469  169  3     | 5     246   89  |
:----------------+------------------+-----------------:
| 3    5     8   | 246   7    246   | 1     9     46  |
| 479  479   2   | 1     569  4569  | 46    8     3   |
| 6    1     49  | 8     3    49    | 2     5     7   |
'----------------'------------------'-----------------'

From there you have a bunch of options to continue, including some simple moves that reduce it to singles. One of them is explained below, but hidden in case you don't want spoilers.

One-step solution: Show

Code: Select all

.------------------.------------------.--------------------.
|   79   379   5   | 679   4    8     |  36    1       2   |
|   2    8     347 | 67    56   1     |  9     346     456 |
| a[4]9  6     1   | 3     2    59    |  8     7       5-4 |
:------------------+------------------+--------------------:
|   18   234   6   | 5     19   247   |  347   234     89  |
|   5    2349  349 | 2469  8    24679 |  3467  2346    1   |
|   18   2479  479 | 2469  169  3     |  5     246     89  |
:------------------+------------------+--------------------:
|   3    5     8   | 246   7    246   |  1     9     d(4)6 |
|  b479  479   2   | 1     569  4569  | c46    8       3   |
|   6    1     49  | 8     3    49    |  2     5       7   |
'------------------'------------------'--------------------'

Turbot Crane:

(4)r3c1 = r8c1 - r8c7 = (4)r7c9 => -4 r3c9; stte

[pingu]

thank you space!


those red 6s can be eliminated by the ones in the blue block I think
About that 9 once i see something i cannot forget, i checked multiple ways that eliminated that 9 but i am not sure plus I didn't go for combination of candidates moves yet.

yea there are triples in the last column from there was easy to finish thank you space