Easy
Naked Single
Only one digit remains possible for this cell — place it.
Single Combination
This run's remaining sum has exactly one digit combination left — every empty cell must draw from it. The classic "17 in two cells is 8+9" move.
Hidden Single
A digit guaranteed to appear somewhere in this run has only one cell left that can hold it.
Medium
Combination Elimination
A digit that appears in none of this run's remaining sum combinations can be ruled out of every cell in it.
Run Bounds
Test one candidate against the smallest and largest distinct totals the other cells can still make. If the needed remainder lies outside those bounds, remove it.
Partner Check
Only two cells of this run are empty, so they split the remaining sum between them — a digit whose partner (remaining sum minus it) can't go in the other cell is impossible.
Naked Pair
Two cells in a run share the exact same two candidate digits — remove those digits from the rest of the run.
Hard
Hidden Pair
Two digits guaranteed to appear in this run only fit in the same two cells — strip those cells down to just those two.
Arrangement Check
A combination has to fit the cells, not just the total: if every combination containing this digit leaves some other cell in the run with nothing it can take, the digit is impossible here. Two or three combinations to weigh.
Naked Triple
Three cells in a run whose candidates combine to exactly three digits — eliminate those digits elsewhere in the run.
Naked Quad
Four cells in a run whose candidates combine to exactly four digits — eliminate those digits elsewhere in the run.
Expert
Hidden Triple
Three guaranteed digits only fit in the same three cells of a run — strip those cells down to just those three.
Hidden Quad
Four guaranteed digits only fit in the same four cells of a run — strip those cells down to just those four.
Arrangement Check (Wide)
The same fit-the-cells check on a run offering four to six combinations — enough that you have to write them out and cross off rather than compare them in your head.
Surface Sum
Two overlapping groups of runs differ by exactly one cell — subtracting their clue totals determines that cell's digit outright.
Extreme
Arrangement Check (Very Wide)
The same fit-the-cells check on a run offering seven or more combinations. Every one of them has to be dealt out against the run's cells, for each candidate you are testing.
Surface Pair
Two overlapping groups of runs differ by two cells — subtracting their clue totals fixes those cells' sum (or difference), ruling out any digit with no possible partner.
Surface Triple
Two overlapping groups of runs differ by three cells — subtracting their clue totals ties those three digits together, ruling out any that can't be completed.
Agreement
Whichever of a cell's candidates turns out true, every surviving line of play forces the same digit onto some other cell — so commit it.
Contradiction
Placing this digit here forces some run into an impossible position — so it can be ruled out.