GridWits

Killer Sudoku techniques

31 techniques, all of which the solver can spot for you as a Smart Hint. Each one has a worked example.

Easy

Naked Single

Only one candidate remains for a cell — place it.

Hidden Single

A digit has only one possible cell left in a row, column, or box — even if that cell has other candidates.

Killer Combinations

A cage's total and size limit which distinct digit sets can live in it.

Innies (Rule of 45)

Every row, column and box totals 45. Subtract the cages inside it; one leftover cell is then known outright.

Outies (Rule of 45)

The cages touching a house cover it plus a spill. When the spill is one cell, their excess over 45 is that cell.

Naked Pair

Two cells in a house sharing the same two candidates lock those digits away from the rest.

Hidden Pair

Two digits confined to the same two cells in a house clear those cells of everything else.

Medium

Pointing Pair/Triple

A digit confined to one row or column within a box is eliminated from the rest of that line.

Box-Line Reduction

A digit confined to one box within a row or column is eliminated from the rest of that box.

Captured Candidates

If every way of making a cage's total uses some digit, that digit is in the cage — and nowhere else in its house.

Naked Triple

Three cells in a house between them using only three candidates lock those digits away from the rest.

Hidden Triple

Three digits confined to the same three cells clear those cells of everything else.

Hard

Cage Placement Support

A digit survives only if a complete cage assignment can place it in that particular cell.

Innies/Outies (2+ cells)

When several cells are left over after subtracting a house's whole cages, their total constrains all of them at once.

Multi-House Rule of 45

Two rows total 90, three total 135 — bands of houses have whole cages to subtract where a single house has only fragments.

Cage Splitting

A cage crossing a house boundary is cut into two parts, each with its own known total.

Cage/Unit Overlap

If every live cage assignment puts a digit in its overlap with a house, that digit leaves the rest of the house.

Cage Comparison

Compare two cages sharing a house and discard assignments that cannot coexist without repeating a digit.

Naked Quad

Four cells in a house between them using only four candidates lock those digits away from the rest.

Hidden Quad

Four digits confined to the same four cells clear those cells of everything else.

X-Wing

A digit restricted to the same two columns in two rows is eliminated from those columns elsewhere.

Expert

Rule of Parity

A region's total fixes how many odd digits it holds, mod 2 — which can force a single undecided cell either odd or even.

XY-Wing (Y-Wing)

A pivot of two candidates with two wings sharing one each — the digit they have in common falls anywhere seeing both.

W-Wing

Two cells with the same pair, joined by a strong link — the digit not in the link falls anywhere seeing both.

XYZ-Wing

Like XY-Wing, but the pivot keeps a third candidate — so the elimination needs cells that see all three.

Swordfish

Three rows whose homes for a digit occupy just three columns — the digit falls from those columns elsewhere.

Extreme

Simple Colouring

Two-colour a digit's conjugate-pair chain; a colour that contradicts itself dies, and cells seeing both colours lose the digit.

Jellyfish

Four rows whose homes for a digit occupy just four columns.

X-Chain

One digit, an alternating chain that both starts and ends on a strong link — so one of its two ends holds the digit.

XY-Chain

A chain of two-candidate cells; when both ends carry the same spare digit, one of them must be it.

X-Cycles

An X-Chain closed into a loop. Closure is what upgrades it: the loop can eliminate along every weak link, or settle one cell outright.