## Need help with a puzzle

Post the puzzle or solving technique that's causing you trouble and someone will help

### Need help with a puzzle

Hi. I'm a new Sukoku player and I can work my way to identifying all possible numbers and eliminate extraneous options from twins. I still get stuck with triplets. This puzzle is from the Sukoku for Dummies book (puzzle 186) and I have the solution, but I can't figure out how to get there without guessing.

I entered the puzzle into Simple Sudoku to confirm that I had narrowed it down to all the possible options. Can anyone give me some tips on how to progress?

-------------------------------------------------------------------------
| 139 | 6 | 8 || 14 | 5 | 2 || 49 | 7 | 13 |
| 123 | 124 | 127 || 6 | 17 | 9 || 48 | 5 | 138 |
| 159 | 14 | 157 || 147 | 8 | 3 || 2 | 149 | 6 |
-------------------------------------------------------------------------
| 4 | 12 | 6 || 157 | 127 | 15 || 3 | 8 | 9 |
| 8 | 5 | 9 || 3 | 4 | 6 || 1 | 2 | 7 |
| 7 | 3 | 12 || 19 | 129 | 8 || 5 | 6 | 4 |
-------------------------------------------------------------------------
| 1256 | 7 | 3 || 159 | 19 | 145 || 468 | 14 | 1258 |
| 156 | 8 | 145 || 2 | 3 | 7 || 469 | 149 | 15 |
| 125 | 9 | 1245 || 8 | 6 | 145 || 7 | 3 | 125 |
-------------------------------------------------------------------------

Mary
memagnus

Posts: 2
Joined: 28 December 2005

Hi, Mary

You missed a couple of pairs

Locked candidate 4 in box 2
(In col 4, r13(4) eliminates r7)
i.e. r7c4={159}

Locked candidate 9 in box 8
(In row 7, c45(9) eliminates c78)

Which leaves us here

Code: Select all
`+-----------------+---------------+----------------+| 139   6    8    | 14   5    2   | 49   7    13   || 123   124  127  | 6    17   9   | 48   5    138  || 159   14   157  | 147  8    3   | 2    149  6    |+-----------------+---------------+----------------+| 4     12   6    | 157  127  15  | 3    8    9    || 8     5    9    | 3    4    6   | 1    2    7    || 7     3    12   | 19   129  8   | 5    6    4    |+-----------------+---------------+----------------+| 1256  7    3    | 159  19   145 | 468  14   1258 || 156   8    145  | 2    3    7   | 469  149  15   || 125   9    1245 | 8    6    145 | 7    3    125  |+-----------------+---------------+----------------+`

At which point I am in over my head.

Mac
QBasicMac

Posts: 441
Joined: 13 July 2005

One step using Almost locked sets xz rule
look at this post http://forum.enjoysudoku.com/viewtopic.php?t=2510

use the sets that I marked.
Code: Select all
`+----------------+----------------+----------------+| 139  6    8    |^14   5    2    | 49   7    13   | | 123  124  127  | 6    17   9    | 48   5    138  | | 159  14   157  |^147  8    3    | 2    149  6    | +----------------+----------------+----------------+| 4    12   6    |*157  127 *15   | 3    8    9    | | 8    5    9    | 3    4    6    | 1    2    7    | | 7    3    12   | 19   129  8    | 5    6    4    | +----------------+----------------+----------------+| 26   7    3    | 159  19   145  | 68   14   28   | | 156  8    145  | 2    3    7    | 469  149  15   | | 125  9    1245 | 8    6    14   | 7    3    125  | +----------------+----------------+----------------+`
bennys

Posts: 156
Joined: 28 September 2005

That's over my head, and I would think not required in a book called "Sudoku for Dummies"...

From the previous candidate list, there's a naked quad (1459) in row 7 allowing you to remove those candidates from all other cells in that row.
This gives you locked candidates - in row 7, the only place for a 5 is in box 8, so all other 5s in box 8 (apart from row 7) can be removed.

That's as far as I could get too. Simple Sudoku couldn't give any more hints. Dubbed into Pappocom Sudoku, I'm told the clues do not form a valid puzzle - if I try 1 in r6c4 I'm told it's invalid, and if I try 9 it's accepted. Dubbed into Sadman Sudoku I'm told there IS only 1 solution, but it gives the next step as a guess.

I believe from what you have above, you can apply forcing chains, but I'm only learning the technique, so I may be wrong in saying that's the way to go. If you try a 1 in r6c4, it'll eventually lead you to a state where r6c4 is 1, and r4c5 is 5, leaving r4c6 with no candidates. So r6c4 cannot be 1, and must be 9. I'll get an argument here, but to me that's guessing - there's no logical next step, so you have to pick a cell and try a number, and continue down that path until you either solve the puzzle or run into an impossible situation.

So, getting back to my first statement, I also think "forcing chains" is a technique not appropriate for a book called "Sudoku for Dummies", so I'm wondering if the publisher believes a guess is an acceptable technique. Out of interest, what's the difficulty rating given to that puzzle? (and, would you mind double-checking to make sure you've copied all the numbers correctly, and possibly posting the original puzzle as it appears in the book, without your own progress?)
Shazbot

Posts: 220
Joined: 24 September 2005

Thanks for the tips so far. I don't understand the "naked quad" concept, so will do some searching for more info.

This puzzle is rated "tough" in the book. The levels are "easy", "tricky", "tough", and "diabolical". Here is the original puzzle, and the solution from the book.

Original Puzzle:
+--------------+--------------+--------------+
| --- 6 8 | --- 5 2 | --- 7 --- |
| --- --- --- | 6 --- 9 | --- 5 --- |
| --- --- --- | --- --- --- | 2 --- --- |
+--------------+--------------+--------------+
| 4 --- --- | --- --- --- | --- 8 9 |
| --- 5 9 | --- --- --- | 1 2 --- |
| 7 3 --- | --- --- --- | --- --- 4 |
+--------------+--------------+--------------+
| --- --- 3 | --- --- --- | --- --- --- |
| --- 8 --- | 2 --- 7 | --- --- --- |
| --- 9 --- | 8 6 --- | 7 3 --- |
+--------------+--------------+--------------+

Solution:

+----------+-----------+------------+
| 9 6 8 | 1 5 2 | 4 7 3 |
| 3 4 2 | 6 7 9 | 8 5 1 |
| 5 1 7 | 4 8 3 | 2 9 6 |
+----------+-----------+------------+
| 4 2 6 | 7 1 5 | 3 8 9 |
| 8 5 9 | 3 4 6 | 1 2 7 |
| 7 3 1 | 9 2 8 | 5 6 4 |
+----------+-----------+------------+
| 2 7 3 | 5 9 1 | 6 4 8 |
| 6 8 4 | 2 3 7 | 9 1 5 |
| 1 9 5 | 8 6 4 | 7 3 2 |
+----------+-----------+------------+

Thanks again, Mary
memagnus

Posts: 2
Joined: 28 December 2005

wow - that IS a toughie! I'd hate to see the diabolicals!

Try going to one of these two sites to learn some new techniques:
http://www.simes.clara.co.uk/programs/sudokutechniques.htm
http://www.angusj.com/sudoku/hints.php
Shazbot

Posts: 220
Joined: 24 September 2005

The strategy suggested by bennys removes 1 as a candidate for r6c4, which leaves 9 as the sole candidate for the cell. This helps but doesn't solve the problem. Here's a more complete solution:

Code: Select all
` . 6 8 | . 5 2 | . 7 .  . . . | 6 . 9 | . 5 .  . . . | . 8 3 | 2 . 6 -------+-------+------  4 . 6 | . . . | 3 8 9  8 5 9 | 3 4 6 | 1 2 7  7 3 . | 9 . 8 | 5 6 4 -------+-------+------  . 7 3 | . 9 . | . . .  . 8 . | 2 3 7 | . . .  . 9 . | 8 6 . | 7 3 .   139    6     8 |   14    5    2 |   49    7   13   123  124   127 |    6   17    9 |   48    5  138   159   14   157 |  147    8    3 |    2  149    6 -----------------+----------------+---------------     4   12     6 |  157  127   15 |    3    8    9     8    5     9 |    3    4    6 |    1    2    7     7    3    12 |    9   12    8 |    5    6    4 -----------------+----------------+---------------    26    7     3 |   15    9  145 |   68   14   28   156    8   145 |    2    3    7 |  469  149   15   125    9  1245 |    8    6   14 |    7    3  125 1. Consider the cell r2c2.When it contains the value 2, the values 1 and 7 in Row 2 must occupy the cells r2c3 and r2c5 in some order.When it contains the value 4, the value 1 in Box 1 must occupy the cell r3c2.Whichever value it contains, the cell r2c1 cannot contain the value 1.- The move r2c1:=1 has been eliminated.Consider the chain r2c9-8-r7c9-2-r7c1-<6|3>-r2c1.When the cell r2c9 contains the value 3, so does the cell r2c1 - a contradiction.Therefore, the cell r2c9 cannot contain the value 3.- The move r2c9:=3 has been eliminated.The cell r2c1 is the only candidate for the value 3 in Row 2.2. The cell r1c9 is the only candidate for the value 3 in Row 1.3. The value 2 in Box 7 must lie in Column 1.- The move r9c3:=2 has been eliminated.Consider the chain r2c5-7-r2c3-2-r6c3-1-r6c5.When the cell r2c5 contains the value 1, so does the cell r6c5 - a contradiction.Therefore, the cell r2c5 cannot contain the value 1.- The move r2c5:=1 has been eliminated.The value 7 is the only candidate for the cell r2c5.`
rubylips

Posts: 149
Joined: 01 November 2005