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MAKE YOUR NEXT MOVE MAKE SENSE

A little logic
goes a long way.

Letters change the look, not the logic. Learn what a deduction means, see a candidate example, and bring it back to your board. Start with singles; move on to pairs and chains when you’re ready.

01 · Start here

Scanning

Choose one letter. Inspect its existing placements to rule out empty cells in the same row, column and box. Look for a forced position.

02 · Naked single

One Choice

An empty cell has exactly one legal candidate after checking its row, column and box. Place that letter.

03 · One location

Hidden Single

Within one unit, a letter is possible in exactly one cell. That cell must contain it, even when other letters are also pencilled there.

04 · Two cells, two letters

Naked Pair

Two cells in the same unit each have exactly the same two candidates. Those letters must occupy those cells, in some order. Eliminate them from the other cells of that unit.

05 · Two letters, two locations

Hidden Pair

In one unit, two letters are possible only in the same two cells. Keep those letters in those cells and remove their other candidates.

06 · Locked candidates

Interaction

Pointing: all positions for a letter in a box lie in one row or column, so exclude it from the rest of that line. Claiming: all positions in a line lie in one box, so exclude it from the rest of that box.

07 · Three cells, three letters

Naked Triple

Three unsolved cells in one unit have only three different candidates between them. Each cell may have two or three of them. Remove these letters from all other cells in the unit.

08 · Three letters, three locations

Hidden Triple

Three letters are confined to three cells of a unit. Remove all other candidates from those cells. Every letter need not occur in every one of the three cells.

09 · Four cells, four letters

Naked Quad

Four unsolved cells in one unit collectively allow only four letters. Eliminate those four letters from every other cell in that unit.

10 · A rectangle for one letter

X-Wing

Find two rows in which a particular letter has exactly two possible columns, the same two in both rows. Eliminate that letter from those columns in other rows. The rule also works with rows and columns swapped.

11 · Also called XY-Wing

Y-Wing

A pivot {A,B} sees two wings {A,C} and {B,C}. Each cell has exactly two candidates. Whichever pivot letter is chosen, one wing is C. Remove C from other cells that see both wings.

12 · Linked two-candidate cells

XY-Chain

Follow cells that each have exactly two candidates, with successive cells seeing one another. Each forced second candidate links to the next cell. If the endpoints share a letter and excluding it at one end forces it at the other, remove it from cells seeing both ends.

Work through a deduction →