Sudoku solving techniques

Every technique this engine uses, in the order it tries them — cheapest first, which is also roughly the order a person learns them. Each page has a worked example taken from a real puzzle in our bank, not a diagram drawn by hand.

Singles

Place a digit outright. Every puzzle is mostly these.

• Full House A house with one empty cell left. The first thing anyone learns.
• Hidden Single A digit with only one home left in a house, even though that cell has other candidates.
• Naked Single A cell with only one candidate left.

Locked candidates and subsets

Eliminate rather than place. This is the real step up.

• Pointing A digit confined to one line inside a box clears that digit from the rest of the line.
• Claiming A digit confined to one box inside a line clears that digit from the rest of the box.
• Naked Pair Two cells in a house holding the same two candidates lock those digits away from the rest.
• Hidden Pair Two digits that can only go in the same two cells own them, whatever else those cells show.
• Naked Triple Three cells sharing three candidates between them lock those digits away.
• Hidden Triple Three digits restricted to the same three cells clear everything else out of them.
• Naked Quad Four cells sharing four candidates between them. Rare, and usually preempted.
• Hidden Quad Four digits confined to four cells. The rarest subset in practical play.

Fish and wings

Patterns that span the whole grid rather than one house.

• X-Wing One digit, two rows, two columns. The first pattern that spans the whole grid.
• XY-Wing A pivot and two pincers. Whichever way the pivot falls, one pincer takes the digit.
• XYZ-Wing An XY-Wing whose pivot holds all three digits, so targets must see all three cells.
• Swordfish An X-Wing with three rows and three columns instead of two.
• Simple Colouring Follow one digit's forced chain through the grid in two alternating colours.

Chains

Follow an either-or argument across the board.

• Jellyfish The four-row fish. Valid, beautiful, and almost never necessary.
• XY-Chain A run of two-candidate cells that returns to the same digit at both ends.

How difficulty is decided

A puzzle's band is the hardest technique it actually requires — not how many clues were removed. Clue count barely predicts difficulty: measured across 1,200 puzzles from a clue-count-based generator, the correlation with required logic was −0.368, and at a fixed 30 clues the necessary technique ranged from plain singles all the way to XY-chains.

So Very Easy means singles only, Hard means you will need an X-Wing or an XY-Wing somewhere, and Master means an XY-chain. Nothing here ever needs guessing.