Sudoku master needed

Thirith

As an occasional Sudoku player and auto-didact, I find that with the difficult ones I often get to a point where I simply don't know how to proceed. I know various tricks how to get as far as possible, but at this point I'm usually reduced to making an educated guess.

Which is why I was wondering if there might be a Sudoku sensei here that could help me get the black belt. Take for instance the Sudoku here:



How do I proceed from this?

knitdan

This may not help you, but back when I did these on paper and I got to a point like this, I'd make a guess in pencil and work from that in pencil until i either ran into a blockage or finished the puzzle.

Now how do you pick which one to guess on? I try and complete rows and squares. That vertical row with 237 has only 3 blank spaces. The upper right and far right squares are only missing two spaces each.

Also, I try to break it down by number. Fill in all the 1s then the 2s then the 3s etc. get stuck, move on to next number.

Daimar

Thirith wrote: »

As an occasional Sudoku player and auto-didact, I find that with the difficult ones I often get to a point where I simply don't know how to proceed. I know various tricks how to get as far as possible, but at this point I'm usually reduced to making an educated guess.

Which is why I was wondering if there might be a Sudoku sensei here that could help me get the black belt. Take for instance the Sudoku here:



How do I proceed from this?

I cheated and punched it into an online solver and based on the numbers you have solved it said that there is a unique solution but there is no logical way to solve it within the limits of the program, so it essentially solved and checked it using guesses. There was the caveat that just because the program couldn't solve it logically didn't mean there wasn't a logical solution, but I take that to mean you have to hold so many numbers in your head at once with a ton of "if/and" type logic statements that you eventually get to a point where you're just guessing on the 4 & 6 in the top right or 2 & 8 on the mid right sections then running all the possibilities in your head to check them. Not a lot of help, but I stared at it for probably 10 minutes and ran out of all my usual tricks for solving these using logic.

Echo

That image looks like how I brute-force them with pen and paper.

Write 1-9 in all empty squares, then strike out the numbers that can't go in that square, and work from there.

And related, two Sudoku-like games I enjoy are 0hh1 and 0hn0.

Thirith

I was kinda afraid that there is a point at which there are no more tricks and the only thing that works is brute force. It's a shame, because at that point they are no longer enjoyable to me. I enjoy the bit where you look at every square, row and column to see if there's some information there that in combination with other information allows you to reduce the number of options, but not when the last part becomes a chore that requires patience but no brains.

ceres

I recommend nonograms (picross). You can find very simple ones and very complex ones, but I like making pictures more than doing obvious math so they work out really well for me.

Thirith

Nonograms are fun, but they're not so much my thing. I don't much play Sudoku on my own anyway; it's usually if I'm going somewhere with my wife and she needs something to take her mind off some things, and that's where a tricky Sudoku tends to work wonders. We usually take turns - she does three numbers, I do three - but that's another reason why the point where brute force is needed breaks the flow.

knitdan

Yeah this kind of becomes the issue with Sudoku, making it "harder" generally means removing more numbers from the puzzle to start with and that usually means it's less likely to be able to completely solve it through logic and at some point you'll have to guess.

CelestialBadger

A well-designed Sudoku should be solveable with logical techniques.

djmitchella

http://www.su-doku.net/tech2.php has some less obvious ways to link squares together, in case you hadn't seen those ones before.

Thirith

These are intriguing! I'll have to check them out and see if they help - though, more importantly, I'd want to understand why they work.

garroad_ran

Damnit, ignore this!

Savant

I'm not much of an sudoku expert or player, but looking at those linked techniques it looked like a variation of the coloration technique will let you fill out some more numbers. It's like doing a branching path for logic puzzles where you go down a bit on two mutually exclusive but comprehensive paths and see if you get contradictions or consistencies on those paths to eliminate extraneous possibilities.

In particular for the posted puzzle:

There are four different 3s remaining on the board, and the middle column has two spots where a 3 has to be placed. If you do the coloring technique where you run down a chain of where the rest of the 3s will have to go for each possibility, you'll find one of those colors has no valid spots to put the last 3. So that means that you can deduce which of middle column 3s is correct, then fill in a bunch more 3s as a consequence.

Thirith

Thanks, that makes sense. Mind you, it's more difficult to do with a Sudoku app while traveling - or at least my brain can only hold so many branches of a logic path at the same time.

Smasher

Note: Rows are numbered from the top, Columns from the left. 3x3 groups of Cells are Blocks. Cells are identified as Row/Column in the format R#C#.

Here's one way to progress:

Assume that R9C7 is not 9.
- The only other place for a 9 in Row 9 is R9C2, so that must be 9.
- Since R9C7 is not 9, R9C7 and R7C7 form a twin pair (5/8).
- That means R4C7 is not 8, so it must be 9.
- R5C9 is in the same Block as R4C7 and can no longer be 9, so it's 8.
- Row 5 now has only one place for a 9, in R5C2, so that must be 9.
- We've determined that R5C2 and R9C2 are both 9s, but they're both in column 2 which is a contradiction.
Our assumption that R9C7 is not 9 is therefore false, so it is 9.
It follows that R4C7 is 8 and R5C9 is 9, which eliminates 9 as a possibility in R5C2. R9C7 eliminates 9 as a possibility in R9C2, which leaves R5C2 and R9C2 as a 2/5 twin pair which eliminates a fair number of possibilities.

ArbitraryDescriptor

Smasher wrote: »

Note: Rows are numbered from the top, Columns from the left. 3x3 groups of Cells are Blocks. Cells are identified as Row/Column in the format R#C#.

Here's one way to progress:

Assume that R9C7 is not 9.
- The only other place for a 9 in Row 9 is R9C2, so that must be 9.
- Since R9C7 is not 9, R9C7 and R7C7 form a twin pair (5/8).
- That means R4C7 is not 8, so it must be 9.
- R5C9 is in the same Block as R4C7 and can no longer be 9, so it's 8.
- Row 5 now has only one place for a 9, in R5C2, so that must be 9.
- We've determined that R5C2 and R9C2 are both 9s, but they're both in column 2 which is a contradiction.
Our assumption that R9C7 is not 9 is therefore false, so it is 9.
It follows that R4C7 is 8 and R5C9 is 9, which eliminates 9 as a possibility in R5C2. R9C7 eliminates 9 as a possibility in R9C2, which leaves R5C2 and R9C2 as a 2/5 twin pair which eliminates a fair number of possibilities.

Guessing right is the worst. You want to fail asap, so if you can spot a square that has very few possibilities; rather than test from those spaces, test from spaces that rule those out. It also helps if you just do a pass considering only thr trial number. The above is a good example of 9s breaking nines; I went for 3's.

Why? That's really the question here, right?

Because there's very few options for three in Top Right, Top Center, Bottom Right, Bottom Center. And those also make a nice square, which is a perfect storm. Since each corner affects the other two (particularly so in this specific case), each guess has an immediate impact vertically and horizontally so it's quick to visualize/trial.

In my check, a 3 in the wrong spot in TR,TC,BC eliminated all possibilities in BR.

When I do these on paper, I just go number by numbers. All the 1s I can spot, 2s, etc, and I note how many of each I've found in the form of noting the missing numbers outside the square; sorry center square. So when I get stuck, I can start on the most guessable. 3-5 is usually fertile ground. Less than that and you're usually better off testing other numbers that impact their candidates, because they're probably either deadlocked or diagonal. More than that and you're probably still pretty wide open.

(But I'd be lying if I said any of that logic ever stopped me from wasting 30 minutes trying to dead reckon a puzzle with plenty of deterministic gimmes unfilled)

Thirith

Thanks again for all the helpful information!