The New Sudoku Players' Forum

[vidarino]

I think u can solve using remote pair.

Hmm, no, I don't think you can. There is an even number of pairs leading to and from R4C5, and the remote pairs rule only works on chains with an odd number of links.

However, the easy way out of this one is the BUG+1 principle; If you have one multivalue (more than two candidates) cell and the rest of the grid is bivalue (two candidates) cells, you can set the multivalue cell to whichever of the candidates that occurs three times in its row, column and box. So in this case, R4C5=1. It's hard to explain why this works, but it does. Search the forum for "BUG" if you want to dig deeper. (EDIT: Or follow the link in Tracy's post. )

A less easy way out is to use a forcing chain or nice loop. There are plenty of starting points, but one example is;
R4C4-1-R8C4-6-R7C5-1-R7C8-3-R6C8-1-R5C7-3-R5C5-1-R4C4

It basically means that if R4C4=1, then R5C5 is 1 too, which is a contradiction. So R4C4 must be 6, and I believe the rest will follow quickly thereafter.

Vidar

[QBasicMac]

Here is another puzzle that I have no clue as to what to do next.

Hi, throbdude,

Say, it would be VERY helpful if you would post "another puzzle" in a separate thread whenever you have one. This thread should have been reserved for the initial puzzle you posted and comments about it.

Otherwise, I keep getting emails and don't want to unscribe because I am interested in the first puzzle. But now they come because of the second.

So, one question or puzzle per thread is a helpful practice.

Right?

Mac

P.S. Too late to fix this one. We just have to continue addressing two problems at the same time.

[tso]

Kent is actually right on this one!


Though BUG is obviously the best most magical way to solve from this postion, the four bracked [13] cells make r5c5 and r7c8 a remote naked pair. They intersect at r7c5, exluding 1 from that cell, solving the puzzle.

Code: Select all

 *--------------------------------------------------*
 | 5    4    1    | 3    2    6    | 9    8    7    |
 | 7    6    9    | 8    5    1    | 2    4    3    |
 | 3    2    8    | 9    7    4    | 6    5    1    |
 |----------------+----------------+----------------|
 | 9    13   4    | 16   136  7    | 5    2    8    |
 | 8    5    7    | 4   [13]  2    |[13]  9    6    |
 | 6    13   2    | 5    9    8    | 7   [13]  4    |
 |----------------+----------------+----------------|
 | 4    9    36   | 7    16   5    | 8   [13]  2    |
 | 2    8    36   | 16   4    9    | 13   7    5    |
 | 1    7    5    | 2    8    3    | 4    6    9    |
 *--------------------------------------------------*

Another choice is a 5 cell xy-type forcing chain, marked in brackets above. ANY value in ANY bracketed cell will exclude the candidate 1 from r5c5, solving the puzzle.

Code: Select all

 *--------------------------------------------------*
 | 5    4    1    | 3    2    6    | 9    8    7    |
 | 7    6    9    | 8    5    1    | 2    4    3    |
 | 3    2    8    | 9    7    4    | 6    5    1    |
 |----------------+----------------+----------------|
 | 9    13   4    |[16]  136  7    | 5    2    8    |
 | 8    5    7    | 4   {13}  2    |[13]  9    6    |
 | 6    13   2    | 5    9    8    | 7    13   4    |
 |----------------+----------------+----------------|
 | 4    9    36   | 7    16   5    | 8    13   2    |
 | 2    8    36   |[16]  4    9    |[13]  7    5    |
 | 1    7    5    | 2    8    3    | 4    6    9    |
 *--------------------------------------------------*

For example:

r4c4=1 -> r5c5=3
r4c4=6 -> r8c4=1 -> r8c7=3 -> r5c7=1 -> r5c5=3
Therefore, r5c5=3

There are many other forcing chains of various lengths.



Still another choice is coloring the 1s:

Code: Select all

 *--------------------------------------------------*
 | 5    4    1    | 3    2    6    | 9    8    7    |
 | 7    6    9    | 8    5    1    | 2    4    3    |
 | 3    2    8    | 9    7    4    | 6    5    1    |
 |----------------+----------------+----------------|
 | 9   +13   4    |+16   136  7    | 5    2    8    |
 | 8    5    7    | 4   +13   2    |-13   9    6    |
 | 6   -13   2    | 5    9    8    | 7   +13   4    |
 |----------------+----------------+----------------|
 | 4    9    36   | 7    16   5    | 8   -13   2    |
 | 2    8    36   |-16   4    9    |+13   7    5    |
 | 1    7    5    | 2    8    3    | 4    6    9    |
 *--------------------------------------------------*

Starting with any cell that can hold a '1' you'd like, label it PLUS. I started with r4c2. Then label any 'conjugates' MINUS. (Two cells are conjugates on a specific candidate if they are the only two cells in that row, column or box that can hold that candidate.) Continue until there are no more conjugates connected with a labeled cell.

Either all the PLUS cells must be 1 OR all the MINUS cells must be 1. Because row 4 and box 5 have more than one PLUS, they cannot be 1. Also, any cell that can 'see' both a PLUS and a MINUS will also be excluded. (The "Remote pairs" tactic is a subset of coloring.)


The point is, once you've reduced the grid to mostly bivalue cells, you nearly always have lots of choices.

[Cec]

"...Though BUG is obviously the best most magical way to solve from this postion, the four bracked [13] cells make r5c5 and r7c8 a remote naked pair. .."

I recently read an explanation about this interesting technique (remote naked pair) in another thread, not implying of course that you haven't been clear here, but would like to know that particular thread or link for future reference. Do you know this source? Help would be appreciated.
Cec

[tso]

I first found it here where the name was coined.

Sudoku Susser's manual also describes it on page 42.

[Cec]

Thanks tso for your prompt reply.
Cec