Sudoku Grove
Sudoku Solving Techniques
Each technique below is a way to place a digit or rule one out. They are in the order you will need them, and each one matches a level on this site.
A word on terms. A unit is any row, column or box. Two squares see each other if they share a unit. A candidate is a digit that has not yet been ruled out for a square.
1. Naked single (easy)
A square that sees eight different digits can only hold the ninth. Check its row, column and box, and if only one digit is missing from all three, write it in. Every easy puzzle on this site can be solved with naked singles alone.
2. Hidden single (medium)
A digit that has only one possible square in a unit must go there, even if that square has other candidates. Example: a box lacks a 3; two of its rows already contain a 3 elsewhere and one column does too, leaving one free square. That square is the 3. Medium puzzles need this at least once.
3. Locked candidates (hard)
Pointing: if, within a box, all the candidates for a digit lie in one row, the digit must be in that row inside the box. So remove it from the rest of that row, outside the box. The same holds for a column.
Claiming (box-line): if, within a row, all the candidates for a digit lie inside one box, then the digit in that box must be in that row. Remove it from the box's other squares.
4. Naked pair (hard)
Two squares in the same unit with exactly the same two candidates, say {4, 8}, must hold those two digits between them. No other square in that unit can be a 4 or an 8, so remove both from the rest of the unit. The idea extends to three squares sharing three candidates (a naked triple).
5. Hidden pair (expert)
If two digits each appear as candidates in only the same two squares of a unit, those squares must hold those two digits. Every other candidate in those two squares can go.
6. X-wing (expert)
Find a digit that, in two different rows, can only go in the same two columns. The four squares form a rectangle, and the digit must sit in two opposite corners, one per row. Either way, both columns are covered, so remove the digit from every other square in those two columns. Swap rows and columns for the mirror version.
7. XY-wing (expert)
Take a square with two candidates, X and Y (the pivot). Find two squares it sees: one with X and Z, one with Y and Z. Whatever the pivot turns out to be, one of those two squares must be Z. So any square that sees both of them cannot be Z.