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# Sudoku/Reddit/January 2020/3D Medusa help

## The question

3D Medusa Help - read comment for specific question :) (see the link for other responses)

So I recently learned the 3D Medusa technique. Can someone please explain why the 7 in the highlighted cell can’t be eliminated? I thought if a number in a cell is colored, then the uncolored numbers can be eliminated if that number is colored in another cell but in the same house (I hope that made sense. This is very hard to explain in words haha).

## Abd responds

The OP did pretty well explaining the question. This puzzle in SW solver, raw. Tough Grade (142)

The OP is using an enjoysudoku.com phone solver. These allow coloring, which vastly improves the solving power available.

Because it should not matter for a 3D Medusa, but for ease of verification, I'm assuming that the OP started by coloring the row pair in 2, making the 2 in r1c1 green and the 2 in r1c7 yellow. These are then chained through strong links. Each new candidate is colored as a direct consequence of the previous colorings of the same candidate. So if the original green candidate is true, all the greens will be true. And if the original yellow candidate is true, all the yellows will be true.

So then we look for interactions. Basically, if both chains eliminate a candidate, it is unconditionally eliminated. If one chain comes to a contradiction, the entire chain is eliminated, showing the other chain as valid. The SW Solver page gives six "rules" but they are all actually obvious.

(The case of both chains confirming a candidate will immediately resolve that candidate as true, unconditionally. So if that is followed, what remains are alternates, which will move toward the whole puzzle being cells with opposite colors in them, as coloring is completed and eliminations are made, until one comes to a contradiction.)

In this case, we know that the 7 in r3c8 is eliminated, the yellow chain provides no such information for that 7. There is no yellow 7 in any cell that cell can see, not yet, anyway. The OP has not completed the possible coloring. So I will see what I can find. I load the puzzle into Hodoku.

Taking the puzzle to the OP's state, I do not see how the 3 in box 3 was resolved. Checking with SW solver, I found no strategy that resolves that 3 as a next step. I suspect this was a lucky mistake. Happens. Or the user did a Nishio on that candidate and found a contradiction. The 3 shown is, in fact part of the solution. I will accept it, to see what is possible from the position the OP had.

## Full solution by extending the coloring

I will color off of the same pair, r1c17, but I continued the coloring far beyond what the OP did. I actually went further than necessary because as soon as one of the mutual confirmations eliminated a colored cell from the other chain, that created, then, an immediate contradiction and the entire contradicted chain would be eliminated. I could also have left the coloring and resolved the mutual confirmations, but I also wanted to show the eliminations, so this is is what I saved as an image:

Colors

• light orange cells: seed pair
• green candidate: first chain
• red candidate: opposite chain
• purple: candidate eliminated by both chains
• light blue cells: mutual resolution (to non-eliminated candidate in it)

I could have continued coloring, but when r3c3 was mutually confirmed, this eliminated a green-colored candidate, r3c2<>3. Because that would only have been colored green if logically necessary if the green chain was valid, the entire green chain is eliminated, not just that particular candidate, and this leaves the puzzle very close to completion. Indeed, it was singles to the end.

## Commentary

A Reddit user: "I'm not a fan of or extensively familiar with 3d medusa stuff, but from my understanding, it's a trial and error type method." 3D Medusa is not a trial and error method. No guessing is involved. Yes, one will decide on a pair to color from, and some colorings will not find a Medusa pattern, but we also decide on what candidates to look at for fish or wings, and some such examinations produce no results and all that is what might be called "taking inventory", not guessing.

"3D Medusa" is a pattern that exists in a puzzle, and it is discovered by looking for it. I have written in the past that Simultaneous Bivalue Nishio is not 3D Medusa, but that may have been a misunderstanding. More accurately, SBN is a method of finding Medusa results. Yes, one must pick a seed pair for SBN. But almost any seed pair in most puzzles will produce some results.

SBN will always simplify solution, but a particular seed choice may be more or less effective at simplifying it so that results are within the solver's reach. The process includes the possibility of making consecutive seed choices. There is skill in choosing an effective seed pair, but the method is surprisingly robust, it is not necessary to choose the "best seed."

## Conclusion

My own understanding of 3D Medusa and SBN has been enhanced by this examination. SBN is 3D Medusa, something that was suggested to me long ago, but I didn't understand at the time. SBN is an approach, a method, and 3D Medusa is a pattern that the method will find. And that pattern can look really, really complicated. But the approach, the method, is terminally simple if coloring is available.

## Debate

A pattern is a recurring design; however, 3D Medusa does not form a specific shape. A method is more fitting to describe a 3D Medusa as it follows a few rules to dictate its expansion.

While 3D Medusa is an extension to Simple Coloring, both only color conjugate pairs. In other words, the entire system is connected via strong links. When a contradiction is found in one colored branch, we know that the other colored branch is true, and can be set as the ground truth.

The key difference is that SBN behaves similar, but not identical, to a Cell Forcing Chain or Unit Forcing Chain depending on its application. Consequently, weak links or strong links do not matter and as such, if a contradiction is found in one color, you cannot set the other colored branch as the ground truth like you would with a 3D Medusa or Simple Coloring. --PseudoFish (talk) 02:26, 19 January 2020 (UTC)