## Bug + n Example(Implemented by my Solver)

Advanced methods and approaches for solving Sudoku puzzles

### Re: Bug + n Example(Implemented by my Solver)

Hi SpAce,

Thanks for spotting my edits and answered patiently.

SpAce wrote:What exactly do you consider non-complex? I don't see anything less complex than the BUG+2 move. In fact, to me it's the least complex and the most elegant one available here. It's also the easiest to spot, by far.

To reply, allow me to quote Sudopedia definition of BUG:
Sudopedia wrote:A Bivalue Universal Grave or BUG is a state of the grid in which every unsolved cell has 2 candidates, without the presence of Hidden Singles.

This is one of the Deadly Patterns that do not occur in a valid Sudoku.

What I understand from Sudopedia definition is that, BUG is one of the deadly patterns, from where there is no other logical move possible at all. But, may be I am wrong.

Is BUG+n move also possible in degenerating case?

I don't understand the question.

Actually, I mean that, is BUG+n move also possible without reaching deadly pattern? (A puzzle state is reached, from where multi-solutions are possible, and there is/are no more logical move(s) possible to solve the puzzle.)

Or, maybe its called HBUG? (When BUG alone can't produce any exclusion.)

R. Jamil
rjamil

Posts: 601
Joined: 15 October 2014
Location: Karachi, Pakistan

### Re: Bug + n Example(Implemented by my Solver)

rjamil wrote:
Hidden Text: Show
To reply, allow me to quote Sudopedia definition of BUG:
Sudopedia wrote:A Bivalue Universal Grave or BUG is a state of the grid in which every unsolved cell has 2 candidates, without the presence of Hidden Singles.

This is one of the Deadly Patterns that do not occur in a valid Sudoku.

What I understand from Sudopedia definition is that, BUG is one of the deadly patterns

Yes, it is. More specifically BUG+0 is a deadly pattern. BUG+1, BUG+2, and any BUG+n (n>0) are not deadly patterns. They're almost deadly patterns. A huge difference.

from where there is no other logical move possible at all. But, may be I am wrong.

A deadly pattern is one where there is NO logical move possible. Thus, if you actually reach a deadly pattern while solving, you've either made a mistake or the puzzle is not valid. A deadly pattern (uniqueness or not) can never exist in its pure form (DP+0, all guardians eliminated) in a valid puzzle. That's why we know at least one of its guardians must be true in the solution, and all DP solving is based on that single fact. It's all about preventing the deadly pattern from forming, or rather, knowing that it can't form (if we know that the puzzle is valid).

Actually, I mean that, is BUG+n move also possible without reaching deadly pattern? (A puzzle state is reached, from where multi-solutions are possible, and there is/are no more logical move(s) possible to solve the puzzle.)

If you read what I said above, you should understand why that question doesn't make any sense.

Or, maybe its called HBUG? (When BUG alone can't produce any exclusion.)

I don't think it has anything to do with it. The whole HBUG concept should be buried anyway, even though it was my idea. All such situations can be solved more cleanly with a BUG-Lite, like I recently did here, and like Cenoman suggested here (though that puzzle had a full BUG+3 available, too). As usual, blue was right.

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Bug + n Example(Implemented by my Solver)

Hi SpAce,

First of all, regret for replying late as I am still confusing in identifying guardian candidates for June 25, 2020 puzzle, as per Cenoman's OTP solution. I see 9 @ r1c7 as guardian candidate too, that's simply eliminate 9 from r3c9, being that if all guardian cells have same guardian candidate then eliminate that guardian candidate from (cells that sees) common peers of all guardian cells.

Secondly, a W-Wing and an XYZ-Wing moves are available, that's unable to solve the puzzle state, but, need not to be considered as BUG+n move at all.

Thirdly, in Cenoman's short tutorial for me:
Cenoman wrote:For a BUG+n, just think that the pattern is a BUG+(n-1)+1 and search a cell that is alone in a sector with an excess candidate. Apply the process of the BUG+1 and then iterate with remaining BUG+(n-1) pattern.

It fits for both 8 and 9 @ r1c7 as guardian candidates. Or maybe, I am still unable to distinguish between them.

And lastly, Cenoman's faulty BUG+Lite claim confuses me a lot. So, thinking again the same puzzle state with same guardian candidate for all three guardian cells solves like RW's simple logic.

R. Jamil
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rjamil

Posts: 601
Joined: 15 October 2014
Location: Karachi, Pakistan

### Re: Bug + n Example(Implemented by my Solver)

rjamil wrote:First of all, regret for replying late as I am still confusing in identifying guardian candidates for June 25, 2020 puzzle, as per Cenoman's OTP solution. I see 9 @ r1c7 as guardian candidate too

Well, it's not. 9r1c7 is a guardian for Steve's BUG-Lite+3 (later identified as such), but not for the full BUG+3 Cenoman used. Its guardians are (8r1c7, 9r1c9, 9r2c7) and there's no ambiguity about that at all.

, that's simply eliminate 9 from r3c9, being that if all guardian cells have same guardian candidate then eliminate that guardian candidate from (cells that sees) common peers of all guardian cells.

Once again, that's ambiguous terminology. Three different cells can't have the same candidate (guardian or not). They can have the same digit. Candidates are instances of a digit that are bound to specific cells, so they can't be shared by different cells. Thus, three different terms for three different concepts: guardian cell, guardian digit, guardian candidate.

In Cenoman's BUG+3 there are three guardian cells (r1c7, r1c9, r2c7), two guardian digits (8 and 9), and three guardian candidates (8r1c7, 9r1c9, 9r2c7). Plain guardian is a synonym for a guardian candidate (not for a guardian digit or a guardian cell).

Secondly, a W-Wing and an XYZ-Wing moves are available, that's unable to solve the puzzle state, but, need not to be considered as BUG+n move at all.

Irrelevant. Any BUG situation can be solved with other techniques, but we're talking about BUGs now, so let's stick to that. The point of using a BUG instead of those other techniques is that it's often easier and more fun for a manual solver. It certainly doesn't mean that it's the only option.

Thirdly, in Cenoman's short tutorial for me

I let Cenoman help with his own tutorial. I wrote mine here. Read that again, and it should also explain how those guardian candidates are identified. That process leaves no doubt that 8r1c7 is a guardian. Since that cell has only three candidates to begin with, it can only hold one guardian, which means 9r1c7 can't be a guardian. The other reason is that there are four 9s in box 3 and two of them (9r1c9, 9r2c7) were already identified as guardians, so the other two 9s in that box must be non-guardians.

And lastly, Cenoman's faulty BUG+Lite claim confuses me a lot. So, thinking again the same puzzle state with same guardian candidate for all three guardian cells solves like RW's simple logic.

Don't worry about the BUG-Lite logic for now. Try to understand the full BUG first. It's simpler because it deals with the full grid.

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Bug + n Example(Implemented by my Solver)

Hi SpAce,

I will try to think BUG+n move that way (i.e., yours and yzfwsf way.)

I have already changed my BUG+1 routine in order to catch BUG+n Type 1 moves. Also, BUG+n Type 2 is clear for me.

R. Jamil
rjamil

Posts: 601
Joined: 15 October 2014
Location: Karachi, Pakistan

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