The New Sudoku Players' Forum

[mith]

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+-------+-------+-------+
| . . . | . . 9 | . 8 . |
| . . . | 7 . . | 6 . . |
| . . . | 8 6 . | . 5 . |
+-------+-------+-------+
| . 9 5 | . . . | . . 4 |
| . . 8 | . . 6 | 5 . 3 |
| 7 . . | . 2 . | 9 . . |
+-------+-------+-------+
| . 8 . | . 1 7 | 4 . 6 |
| 3 . 1 | . . . | . . . |
| . . . | 4 8 . | 2 . . |
+-------+-------+-------+
.....9.8....7..6.....86..5..95.....4..8..65.37...2.9...8..174.63.1.........48.2..

[RSW]

I'll keep my computer solution hidden, since this puzzle was posted only a few minutes ago.
However, I'd appreciate comments about validity of the logic.

Hidden Text: Show

Code: Select all

 +------------------+--------------+-------------+
 | 1456 13567 3467  | 2   345  9   | 137 8   17  |
 | 8    1235  239   | 7   35   135 | 6   4   29  |
 | 1249 1237  23479 | 8   6    134 | 137 5   29  |
 +------------------+--------------+-------------+
 | 26   9     5     | 13  37   38  | 178 26  4   |
 | 124  12    8     | 19 a79-4 6   | 5  b127 3   |
 | 7    136   346   | 15  2    458 | 9   16  18  |
 +------------------+--------------+-------------+
 | 259  8     29    | 359 1    7   | 4   39  6   |
 | 3    4     1     | 6  d59   2   | 78 c79  578 |
 | 569  567   679   | 4   8    35  | 2   139 15  |
 +------------------+--------------+-------------+


(7)r5c5 = (7)r5c8 - (7=9)r8c8 - (9)r8c5 = (9)r5c5 => -4r5c5; btte

[Leren]

Hidden Text: Show

Code: Select all

*-------------------------------------------------*
| 1456 13567 3467  | 2    345  9   | 137  8   17  |
| 8    1235  239   | 7    35   135 | 6    4   29  |
| 1249 1237  23479 | 8    6    134 | 137  5   29  |
|------------------+---------------+--------------|
| 26   9     5     | 13   37   38  | 178  26  4   |
| 124  12    8     | 19  c79-4 6   | 5   b127 3   |
| 7    136   346   | 15   2    458 | 9    16  18  |
|------------------+---------------+--------------|
| 259  8     29    | 359  1    7   | 4    39  6   |
| 3    4     1     | 6   d59   2   | 78  a79  578 |
| 569  567   679   | 4    8    35  | 2    139 15  |
*-------------------------------------------------*

M Ring Type A : (9=7) r8c8 - r5c8 = (7-9) r5c5 = (9) r8c5 => - 4 r5c5; btte

I see it as a loop ie an M Ring Type A - see here.

Leren

[RSW]

I see it as a loop ie an M Ring Type A - see here.

Leren

Thanks. I figured that there had to be a loop equivalent, but didn't know where to look.

It can be interesting when you give the computer the essential rules of chain making, and then turn it loose. Sometimes, the results are surprising. A couple of times now, it's come up with some odd chains, making me wonder if I'd overlooked a rule or two, but they've all turned out to be valid chains so far.

[denis_berthier]

I'd appreciate comments about validity of the logic.

Hidden Text: Show

(7)r5c5 = (7)r5c8 - (7=9)r8c8 - (9)r8c5 = (9)r5c5 => -4r5c5; btte

It's a mere bivalue-chain[3]:

Hidden Text: Show

biv-chain[3]: r5n7{c5 c8} - r8c8{n7 n9} - c5n9{r8 r5} ==> r5c5≠4

[Leren]

RSW wrote : I figured that there had to be a loop equivalent, but didn't know where to look.

That's easy. Just look at your chain and it's obvious that the first and last terms are in the same cell and are connected by a weak link, completing a continuous loop.

So all you have to do is write loop at the end of your chain and your are golden.

Leren

[RSW]

Yes, it was the fact that both ends were the same cell, that made me realize that it had to be some type of loop. However, I'd never spent any amount of time working with loops. So, I wasn't entirely sure what to do with it. Having spent some time thinking about it since posting it, it now makes more sense to me.

[Leren]

Hi RSW

Hodoku's writeup on loops is an easy read with worked examples here.

Leren