GridWits

Futoshiki techniques

20 techniques, 17 of which the solver can spot for you as a Smart Hint. Each one has a worked example.

Easy

Naked Single

Only one candidate value remains for this cell — place it.

Hidden Single

A value has only one possible cell left in this row or column, even though that cell has other candidates too.

Inequality Bound

Across a sign, the smaller cell can't reach the larger cell's biggest candidate, and the larger cell can't drop to the smaller cell's smallest.

Medium

Compound Comparison

A cell below several different cells in its own row or column must leave enough larger values for all of them; the same counting works above several cells.

Naked Pair

Two cells in a row or column share the exact same two candidates — remove those values from the rest of the line.

Naked Triple

Three cells in a row or column whose candidates combine to exactly three values — eliminate those values elsewhere in the line.

Naked Quad

Four cells in a row or column whose candidates combine to exactly four values — eliminate those values elsewhere in the line.

Hard

Hidden Pair

Two values only fit in the same two cells of a row or column — strip those cells down to just those two.

Hidden Triple

Three values only fit in the same three cells of a row or column — strip those cells down to just those three.

Locked Comparison

A high digit is locked into cells that each point through an inequality to the same forced larger digit — that larger digit is locked into the partner cells and can be removed from every cell seeing them all.

X-Wing

A value's only two candidate cells line up in the same two columns (or rows) across two rows (or columns) — eliminate it everywhere else in those columns or rows.

Hidden Quad

Four values only fit in the same four cells of a row or column — strip those cells down to just those four.

Line Consistency

Every way this row or column's remaining values can be ordered while obeying the signs inside it was checked — a value eliminated here appears in none of them.

Expert

XY-Wing

A cell with two candidates links to two other two-candidate cells that share one candidate each with it and one with each other — the shared value can't be in any cell both of those see.

W-Wing

Two cells share the same candidate pair and aren't in the same row or column, but a chain elsewhere forces one of them to one of those values — eliminate the other from any cell both see.

XYZ-Wing

A three-candidate cell links to two two-candidate cells whose combined candidates match it exactly — the shared value can't be in any cell all three see.

Swordfish

A value's candidate cells across three rows (or columns) line up in the same three columns (or rows) — eliminate it everywhere else in those columns or rows.

Cross-Line Consistency

This row or column has only a few orderings left — any one that would leave some other row or column with no way to finish is out, and a value used by none of the survivors can be struck.

Extreme

Jellyfish

A value's candidate cells across four rows (or columns) line up in the same four columns (or rows) — eliminate it everywhere else in those columns or rows.

Cross-Line Forcing

Same as Cross-Line Consistency, but each ordering is also followed through: fill in every value it forces outright, and rule it out if that leaves some other row or column unfinishable.