Hidden single
Pick a digit and a unit — a row, a column or a box. If only one cell in that unit can still hold the digit, it goes there, even if that cell has other candidates too. Every easy sheet on this site is solved with hidden singles alone.
The fastest way to find them is to scan by digit: take 1, look at each box that has no 1 yet, and see where the 1s in neighbouring rows and columns leave room. Then take 2, and so on.
Single candidate
Sometimes a cell is the only place where you notice the deduction: its row, column and box already contain eight different digits, so only the ninth is left. Medium sheets need this at least once; the hint calls it a single candidate.
Pointing pair and box–line reduction
If, inside one box, every possible cell for a digit lies in the same row, then the digit must sit in that row within that box — so it can be removed from the same row in the other two boxes. That is a pointing pair (or triple).
Box–line reduction is the mirror image: if a row’s only cells for a digit all fall inside one box, remove the digit from the rest of that box. These two moves open up most hard sheets.
Naked and hidden pairs and triples
Two cells in one unit whose candidates are exactly the same two digits must take those two digits between them. Remove both digits from every other cell in the unit: that is a naked pair. Three cells whose candidates come from the same three digits form a naked triple.
The hidden version looks at digits instead of cells: if two digits can go only in the same two cells of a unit, those cells hold those digits, and their other candidates can be erased.
X-Wing and Swordfish
Take one digit. If in two different rows it can go in exactly two cells, and those cells sit in the same two columns, the digit occupies opposite corners of that rectangle. Either way, both columns get it in those rows, so remove it from the rest of both columns. The same works with rows and columns swapped.
Swordfish is the three-row version: three rows in which the digit’s possible cells fall into the same three columns. Expert sheets often need one of these exactly once.
XY-Wing and XYZ-Wing
An XY-Wing uses three cells with two candidates each. The pivot holds X and Y; one wing that sees the pivot holds X and Z, the other holds Y and Z. Whatever the pivot turns out to be, one of the wings becomes Z, so any cell that sees both wings cannot be Z.
In an XYZ-Wing the pivot holds all three digits X, Y and Z. The conclusion is narrower: Z can be removed only from cells that see the pivot and both wings.
An order of attack
Scan for hidden singles until nothing moves. Check for single candidates. Then write full notes and look, in order, for pointing pairs, box–line reductions, pairs and triples. Only then search for X-Wings and wings. After every new digit, go back to the top of the list — easy moves reappear all the time.
If you get stuck on a sheet, the hint names the technique the solver would use next. Try to find it yourself before pressing it a second time.