Sudoku Guessing Technique

Mant tme I've run into Sudoku puzzles where I get stuck. But I've discovered a technique that frequently allows me to solve the puzzle quickly. I make an educated GUESS. Since I don't want to write on the puzzle itself, I've purchased some 8.5 X 10 clear plastic picture holders. They're available in most stationary stores, like Office Depot. What I do with a newspaper puzzle is fold one edge so I can slip the puzzle into a plastic window. I then use an erasable marker to write my numbers on the window where I want them. I start with my "guess", which is usually a binary-pair choice. For example, within a box, or a row, or a column, there may be a "naked-pair" which are two numbers, and only thos two, that can go in a pair of boxes in that row, column, or box. For example, 2,7 and nothing else can go there. You make a decision, and write those two numbers onto your window, and see if that alows you to continue solving the puzzle by standard methods. DO NOT guess a 2nd time. Jusu let it play out until one of two things happen: a) you get a solution (good), or b) you get a "conflict", which means some number is already written that conflicts with what you need to write. Of course, if a) occurs, YOU'RE DONE! If you hit a conflict, erase everything on your window, and start again with the pair in reversed locations. In other words, flip the pair's positions. Then try again. If that doesn't work, you'll have to try another binary-pair, if there are any.

The second method is to pick a unitary-pair. That's a pair of cells that can only be one number, but in either position. For example, within a single box, and in either a single row or a single column, you must have a 2, or other single number. Usually there's a matching pair in an adjacent box. If the pairs are in columns, the boxes in the same box-row. If the pairs are in a rows, the boxes must be in a box-column. By "matching pair" I means the empty cells in each pair must line up with the other pair. So, for example, if one vertical pair are in rows 2 and 3, the matching pair must also be in rows 2 and 3, and another neighboring horizontal box.

The following is a sample puzzle, completed until I "got stuck'. My guess was the 2,6 pair remaining in the right-most column, marked with dashes.

• ||=====|=====|=====||=====|=====|=====||=====|=====|=====|| || | | || | 1 | || | | 5 || || | | 3 || 4 | | 8 || | | || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || | | || | 3 | || | | || || 5 | | || | | 6 || | | 4 || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || | | || | | || 3 | | -6- || || | 8 | || | 9 | || | | || ||=====|=====|=====||=====|=====|=====||=====|=====|=====|| || 3 | | || 9 | 8 | || | | || || | 5 | 2 || | | || | | 7 || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || | | || 3 | 4 | || | | || || 6 | 9 | || | | || | 5 | 8 || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || | | || | 6 | || | | 9 || || | | || | | || | 3 | || ||=====|=====|=====||=====|=====|=====||=====|=====|=====|| || | 3 | || 8 | | || | | 1 || || | | || | 5 | 4 || | 9 | || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || | | 5 || | | 9 || | | || || 1 | | || 6 | | || | | 3 || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || | | || | | || | | -2- || || | | || 1 | | 3 || 5 | | || ||=====|=====|=====||=====|=====|=====||=====|=====|=====||

I could have started with the 2,7 missing at the bottom of the center column, especially if I had placed 7 under 2. Anyway, create your What's-Left-Lists and proceed normally. What I've given you is the CORRECT guess. For fun, try it with 2,6 reversed. You should get "stuck" or hit a "conflict".

Here's another example of guessing, but this time with a triad of numbers in a single box.

• ||=====|=====|=====||=====|=====|=====||=====|=====|=====|| || | | || | -4- | 1 || | | || || 5 | | || 6 | | || | | 9 || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || 9 | 6 | || -2- | | || | 1 | || || | | 4 || | 7 | 3 || 5 | | || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || | | || | 5 | -8- || | | || || 1 | | || 9 | | || 6 | | || ||=====|=====|=====||=====|=====|=====||=====|=====|=====|| || | | || | | || | | || || | | 6 || | | 9 || | | || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || | | || | | || | | || || 2 | | 9 || | | || 1 | | 6 || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || | | || | | || | 9 | || || | | || | | || 8 | | || ||=====|=====|=====||=====|=====|=====||=====|=====|=====|| || | | || | | || | 6 | || || | | 2 || | | 5 || | | 4 || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || 4 | 1 | || | | 6 || | | || || | | 7 || 3 | 8 | || 9 | | || ||-----|-----|-----||-----|-----|-----||-----|-----|-----|| || | | 5 || | | || | 8 | 1 || || 6 | | || | | 2 || | | || ||=====|=====|=====||=====|=====|=====||=====|=====|=====||

In this case, there are three numbers missing in B2: 2,4,8. 2 is blocked in C6 by the 2 in R9. 4 is blocked in C4 by the 4 in R2. And 8 is blocked in C5 by the 8 in R7. So there are three possible guesses. I chose (R1,C5) = 4, which forced (R2,C4)= 2, and R3,C6) = 8. They are all marked with dashes. If I has chosen (R2,C4) = 8, I would have forced (R1,C5) = 2, and (R3,C6) = 8. You can figure out the third combination very easily. Finally, I could have started with the binary pair 3,7 in C7 of B9 because R8 must end in 2,5. But I'll leave that for you to try. Have fun.