# What is a good notation for trial-and-error when solving Sudoku on paper?

When solving Sudoku on paper, I sometimes get to the point where I need to resort to guessing or bifurcation. At that point, I might guess one number, and continue solving, changing that guess if I arrive at a contradiction.

I've experimented with a couple of approaches, e.g., circling the guess and writing the consequences more lightly or small in a particular corner of each cell. But none of this works too well, particularly not if I need a second level of guessing.

Is anyone aware of a reliable notation in this situation? Do I need coloured pencils or transparencies?

You could decide to partition the corners and use one for each level, writing even smaller numbers. Or tilting the numbers at different angles. But that sounds boring, why not use Arabic, Roman and Persian/Farsi (oops, there is some digit overlap) numerals at each level?

I consider sudoku puzzles that legitimately require trial and error unpure and stop solving them, but this is a topic for separate questions.

Contrary to @lynxlynxlynx I lost Interest in sudokus, because they were too simple :) I became interested again, when I found sudokus that required guessing,

I developed a simple notation to keep track of hypothetical changes I made on separate lines.

I introduce a guess with a hash mark:

# A2: 1,2


Then I add consequences of the hypothesis with +:

# A2: 1,2 + B2: 5 + C7: 3


When I run into a contradiction, I can easily roll back the last hypothesis:

# A2: 1,2 + B2: 5 + C7: 3 # G9: 1 + H7 3 => CTR => G9: 5
# A2: 1,2 + B2: 5 + C7: 3 + G9: 5


and so on. Of course, When the paper becomes too cluttered, a refresh on a new sheet becomes necessary.

I kept this notation, when I wrote a program to support limited depth hypothesis/disproof/proof, since the puzzles became too hard to solve with paper, pencil and copy machine. I have explained the method for World's Hardest Sudoku in response to another question, if you're interested.

After filling in all the numbers I can deduce without guessing, I lightly fill in every remaining box with all the possible numbers. Now to make a guess I pick one number and mark it with a light dot above it. Then continue, using standard methods to find other numbers, marking all these new numbers with dots. Hopefully one can continue on to either a solution or a contradiction. If the latter, you then erase all the dots and remove the originally-guessed number that's turned out to be impossible.

• Welcome to Puzzling! I have removed the parts of your answer that were about strategies for how to guess, because this question only asks about a method for notating guesses. Commented Nov 11, 2020 at 1:05