## Special

Interesting puzzles can be posted here
Chris17
New kid on the Grid
Posts: 1
Joined: Tue Feb 20, 2007 2:14 pm
Location: Graz

### Special

Hello!
Here is a puzzle with the given digits
{1,2,3} in block 1, block 6 and block 8,
{4,5,6} in block 2, block 4 and block 9 and
{7,8,9} in block 3, block 5, and block 7
in a way that each row and each column contain three digits as
well.
I found a lot of them. Does anyone know if there is a collection of
such puzzles somewhere?

Example(difficult one):

Code: Select all

``````1 . . | 4 . . | 7 . .
. 2 . | . 5 . | . 8 .
. . 3 | . . 6 | . . 9
---------------------
6 . . | 8 . . | 3 . .
. 5 . | . 7 . | . 1 .
. . 4 | . . 9 | . . 2
---------------------
9 . . | 2 . . | 5 . .
. 8 . | . 1 . | . 6 .
. . 7 | . . 3 | . . 4
``````
100400700020050080003006009600800300050070010004009002900200500080010060007003004

Christoph
rep'nA
Hooked
Posts: 49
Joined: Fri Jan 19, 2007 11:37 am
Location: Union City, California

### Re: Special

Chris17 wrote:Hello!
Here is a puzzle with the given digits
{1,2,3} in block 1, block 6 and block 8,
{4,5,6} in block 2, block 4 and block 9 and
{7,8,9} in block 3, block 5, and block 7
in a way that each row and each column contain three digits as
well.
I found a lot of them. Does anyone know if there is a collection of
such puzzles somewhere?

Example(difficult one):

Code: Select all

``````1 . . | 4 . . | 7 . .
. 2 . | . 5 . | . 8 .
. . 3 | . . 6 | . . 9
---------------------
6 . . | 8 . . | 3 . .
. 5 . | . 7 . | . 1 .
. . 4 | . . 9 | . . 2
---------------------
9 . . | 2 . . | 5 . .
. 8 . | . 1 . | . 6 .
. . 7 | . . 3 | . . 4
``````
100400700020050080003006009600800300050070010004009002900200500080010060007003004

Christoph
A good place to start looking for puzzles of this shape might be here.

As for your puzzle, this would be an excellent puzzle to teach somebody about naked pairs. I think I found 11 at the start. After these the puzzle isn't so bad. A swordfish on 5's eliminates 5 from r1c8 and r8c4. An xy-wing in r1c58, r9c8 implies r9c5<>9 and this solves the puzzle.

Alternatively, if one first eliminates [28] from r1c5 (using the naked pair in box 2), then an xy-chain

Code: Select all

``````.---------------.---------------.---------------.
| 1    69E  5689| 4    39D  28  | 7    235  356-|
| 47   2    69  | 1379 5    17  | 146  8    136 |
| 4578 47   3   | 17   28   6   | 124  245  9   |
&#58;---------------+---------------+---------------&#58;
| 6    179  129 | 8    24   1245| 3    4579 57  |
| 238  5    289 | 36   7    24  | 4689 1    68A|
| 378  137  4   | 1356 36C  9   | 68B  57   2   |
&#58;---------------+---------------+---------------&#58;
| 9    1346 16  | 2    468  478 | 5    37   1378|
| 2345 8    25  | 579  1    457 | 29   6    37  |
| 25   16   7   | 569  689  3   | 1289 29   4   |
'---------------'---------------'---------------'
``````
eliminates 6 from r1c9. Locked candidates then removes the 6 from r2c3 and the puzzle is solved.

Nice puzzle Christoph.
"Obviousness is always the enemy to correctness."-Bertrand Russell
Para
Yokozuna
Posts: 384
Joined: Wed Nov 08, 2006 7:42 pm
Location: The Netherlands

### Re: Special

rep'nA wrote: As for your puzzle, this would be an excellent puzzle to teach somebody about naked pairs. I think I found 11 at the start.
It is actually also a good puzzle to practice swordfish at after the naked pairs (actually 12, twice a naked pair in 6 boxes). You could find 6 swordfishes in this puzzle. Of course going to the xy-wing or xy-chain earlier shortens the path considerably.

greetings

Para
rep'nA
Hooked
Posts: 49
Joined: Fri Jan 19, 2007 11:37 am
Location: Union City, California

### Re: Special

Para wrote: It is actually also a good puzzle to practice swordfish at after the naked pairs (actually 12, twice a naked pair in 6 boxes). You could find 6 swordfishes in this puzzle.
Wow! You are indeed correct. 6 swordfishes in a row (on 1,3,4,5,8,9). I don't recall seeing such a puzzle before. I've probably seen a puzzle with 6 swordfishes, but never in a row and all on different numbers.
rep'nA wrote: Nice puzzle Christoph.
Multiply that compliment by 6.
"Obviousness is always the enemy to correctness."-Bertrand Russell