## Solving without using BUG

Advanced methods and approaches for solving Sudoku puzzles

### Solving without using BUG

Knowing that there's much debate as to the acceptability of uniqueness tests, and that the claim is made that any puzzle can be solved without depending on them, I'm curious to see how this puzzle would be solved without applying the obvious BUG removal.

Code: Select all
` 6    45   2    | 37   347  1    | 57   8    9 3    15   7    | 8    2    9    | 4    15   6 8    14   9    | 5    47   6    | 2    17   3----------------+----------------+--------------- 1    2    3    | 4    8    7    | 6    9    5 4    9    8    | 2    6    5    | 1    3    7 5    7    6    | 9    1    3    | 8    2    4----------------+----------------+--------------- 7    68   4    | 13   35   2    | 9    56   18 2    68   5    | 17   9    4    | 3    67   18 9    3    1    | 6    57   8    | 57   4    2`
EnderGT

Posts: 69
Joined: 19 February 2008

### Re: Solving without using BUG

EnderGT wrote:Knowing that there's much debate as to the acceptability of uniqueness tests, and that the claim is made that any puzzle can be solved without depending on them, I'm curious to see how this puzzle would be solved without applying the obvious BUG removal.

Code: Select all
` 6    45   2    | 37   347  1    | 57   8    9 3    15   7    | 8    2    9    | 4    15   6 8    14   9    | 5    47   6    | 2    17   3----------------+----------------+--------------- 1    2    3    | 4    8    7    | 6    9    5 4    9    8    | 2    6    5    | 1    3    7 5    7    6    | 9    1    3    | 8    2    4----------------+----------------+--------------- 7    68   4    | 13   35   2    | 9    56   18 2    68   5    | 17   9    4    | 3    67   18 9    3    1    | 6    57   8    | 57   4    2`

***** SudoRules version 13 *****
6.2..1.89
3.78294.6
8.95.62.3
123487695
498265137
576913824
7.4..29..
2.5.943..
9316.8.42
column c9 interaction-with-block b9 ==> r8c8 <> 1, r7c8 <> 1
nrc2-chain n7{r1c4 r8c4} - n7{r9c5 r9c7} ==> r1c7 <> 7
...naked-singles...
642371589
357829416
819546273
123487695
498265137
576913824
764132958
285794361
931658742
denis_berthier
2010 Supporter

Posts: 1275
Joined: 19 June 2007
Location: Paris

EnderGT: One of several possibilities
Skyscraper: 7 in [r1c4],[r3c8] (connected through [r8c48]) => [r1c7],[r3c5]<>7
Puzzle solved.

I personally prefer the BUG...
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

### Re: Solving without using BUG

denis_berthier wrote:column c9 interaction-with-block b9 ==> r8c8 <> 1, r7c8 <> 1

Not sure about that part, because I think I already applied it...
denis_berthier wrote:nrc2-chain n7{r1c4 r8c4} - n7{r9c5 r9c7} ==> r1c7 <> 7

But this is good. This is one of those patterns that I still haven't gotten used to looking for.
EnderGT

Posts: 69
Joined: 19 February 2008

### Re: Solving without using BUG

EnderGT wrote:I'm curious to see how this puzzle would be solved without applying the obvious BUG removal.

You should try something harder than a BUG:
Code: Select all
`+-------+-------+-------+| 1 . . | . 2 . | . . 3 || . 4 . | . . 5 | . 6 . || . . . | 7 . . | 8 . . |+-------+-------+-------+| . . 5 | 1 . . | . 9 . || 9 . . | . . . | . . 7 || . 7 . | . . 4 | 2 . . |+-------+-------+-------+| . . 6 | . . 9 | . . . || . 8 . | 2 . . | . 1 . || 3 . . | . 5 . | . . 4 |+-------+-------+-------+`

It is solvable with singles after applying a uniqueness technique.
Mauricio

Posts: 1174
Joined: 22 March 2006

hobiwan wrote:EnderGT: One of several possibilities
Skyscraper: 7 in [r1c4],[r3c8] (connected through [r8c48]) => [r1c7],[r3c5]<>7
Puzzle solved.

I personally prefer the BUG...

Ooh, that's good too. Another I'm not used to looking for yet.
EnderGT

Posts: 69
Joined: 19 February 2008

### Re: Solving without using BUG

Mauricio wrote:
EnderGT wrote:I'm curious to see how this puzzle would be solved without applying the obvious BUG removal.

You should try something harder than a BUG:

I'll take a look at that in a second. I posted this puzzle because my solver wouldn't "look past" the BUG and give me a different hint. As I said to the above posters, I'm still learning to look for those other patterns.
EnderGT

Posts: 69
Joined: 19 February 2008

### Re: Solving without using BUG

EnderGT wrote:Knowing that there's much debate as to the acceptability of uniqueness tests, and that the claim is made that any puzzle can be solved without depending on them, I'm curious to see how this puzzle would be solved without applying the obvious BUG removal.

Code: Select all
` 6    45   2    | 37   347  1    | 57   8    9 3    15   7    | 8    2    9    | 4    15   6 8    14   9    | 5    4-7  6    | 2   d17   3----------------+----------------+--------------- 1    2    3    | 4    8    7    | 6    9    5 4    9    8    | 2    6    5    | 1    3    7 5    7    6    | 9    1    3    | 8    2    4----------------+----------------+--------------- 7    68   4    | 13   35   2    | 9    56   18 2    68   5    | 17   9    4    | 3   c67   18 9    3    1    | 6   a57   8    |b57   4    2`

Candidates 2 & 9 have been resolved, so they can't contribute any further. Candidates 1,3,4,5,6 & 8 have two candidates only in each row/column/box, so none of them can individually lead to any further eliminations.

This leaves Candidate 7 and hobiwan's Skyscraper -- or a 2-String Kite (shown above), or an Empty Rectangle (not shown), or any of 50 finned X-Wings (not shown) -- for eliminations based on a single candidate.

I agree with hobiwan, I like the BUG+1.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Solving without using BUG

daj95376 wrote:Candidates 2 & 9 have been resolved, so they can't contribute any further. Candidates 1,3,4,5,6 & 8 have two candidates only in each row/column/box, so none of them can individually lead to any further eliminations.

This is good information. I'll have to remember this when trying to figure out what candidate to attack in the future. Thanks.

daj95376 wrote:This leaves Candidate 7 and hobiwan's Skyscraper -- or a 2-String Kite (shown above), or an Empty Rectangle (not shown), or any of 50 finned X-Wings (not shown) -- for eliminations based on a single candidate.

That's 2 kites that have been pointed out. I really need to get better at seeing those. Empty Rectangle looks like something new for me to read up on. Thanks again!
EnderGT

Posts: 69
Joined: 19 February 2008