## SEW It's the Same - Either Way

Advanced methods and approaches for solving Sudoku puzzles

### SEW It's the Same - Either Way

The reason many of our solving techniques such as Skyscrapers, 2-string Kites and other chaining processes work, is because they examine situations where there are only two possible options, and both lead to the same result somewhere else in the puzzle. So we can take that result as true, even if in the meantime we don't yet know the true arrangement that predicts it. I often us this approach, which I call SEW. Try this:

A.png (13 KiB) Viewed 409 times

Here I was looking at what was going on in Box2. With the 4,5 Locked Pair on the middle shelf, there were only two places for the 6. They worked out as

Table1.png (2.81 KiB) Viewed 409 times

Now what does that mean for the rest of the puzzle? It turned out that the first scenario predicted Row5 to be 297 641 358 and the second forced it to be 297 346 158.
This meant that in either case the 6 in Box5 had to be on the middle shelf, which in turn meant that the 6 in Box6 had to be at r4c8 anyway, which easily solved the whole puzzle.
There are of course many ways to solve this puzzle and you can look up the discussion of it which took place between ravel and RW in 2005 in the post Solving without pencilmarks.
Yogi
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### Re: SEW It's the Same - Either Way

There is no reason to limit yourself to two possibilities leading to the same conclusion. The same idea applies equally well when there are three or more possibilities which all lead to the same conclusion.

There are also parallel ideas that avoid enumerating possibilities and instead look directly at things that are provably true; without going through any explicit enumeration/examination of possibilities. This is how chains are normally thought about, since chains are a more general construct that don't depends on there being exactly two underlying possibilities (at least in the sense you are talking about).

JasonLion
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### Re: SEW It's the Same - Either Way

This puzzle seemed to be more in line with your previous question. Apart from basic mark-offs and singles the puzzle solves in 6 moves :

1. A pointing pair in Row 2

2. A naked triple in Row 2.

3. A pointing pair in Column 5.

4. A naked quad in Box 8.

5. An XWing in r15c47, and

6. A naked pair in Column 7.

Moves 2, 4 and 6 were the subject of your previous question - you might like to practice finding them.

Leren
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### Re: SEW It's the Same - Either Way

Well I'm with the P&P Brigade - the Pen and Paper Sudoku Solvers gang. I like to solve random puzzles I might find in a magazine while sitting in a Doctor's waiting room. No computer, no hand-held divice, no solver program; just me, my pen and that damn puzz. And boy am I gunna sort it out!
So I have of course developed some strategies of my own and that is one of them. But the simplicity of it seems to have been lost. The idea is that if you can find a place in your partly-completed puzzle where there are only two possibilities, and you can show that something else will be true in both cases, then that means it is true in ALL cases. So you have found something which you can move on with and may even solve the puzzle. You don't need to know which of the two starting possibilities was true. That becomes clear later.
Yogi
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### Re: SEW It's the Same - Either Way

1..45..8....7...4.4.62.83..632584...548179632...632854..436.92.29.841.63.6.92.4.8
Here's another one. At this point the puzzle has a Locked Pair 5 & 7 at r79c6. But is it 5 over 7 or 7 over 5?
A quick look at what happens in Boxes 7, 8 & 9 for these two possibilities shows that they both predict r7c1=8
Again it's the Same Either Way. You can then solve the puzzle with 8 at r7c1, without worrying about the Locked Pair.
Yogi
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