Gooby
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Sudoku techniques, step by step

Every puzzle in our app can be solved by logic alone. These are the techniques you need, from your first Easy game to Master — each shown on a real position from one of our puzzles.

Practise in the app Start learning

Words you'll see

  • Unit — a row, a column or a 3×3 box. Each unit holds 1–9 once.
  • Candidates (or notes, pencil marks) — the digits a cell could still be. In the diagrams they are the small numbers.
  • Peers — cells that share a unit with a cell, so they can't hold the same digit.
  • r4c7 — row 4, column 7. Boxes are numbered 1–9 left to right, top to bottom.

Most techniques don't place a digit directly. They remove candidates, and the removals then expose a single. In the diagrams, the pattern is shaded blue, removed candidates are red and struck through, and a placed digit is green.

Singles — the bread and butter

Hidden Single Easy

Pick a digit and a unit. If the digit fits in only one cell of that unit — every other cell is filled or already sees that digit — it must go there, even if the cell has other candidates. Scanning each box for each digit finds most of the moves in an easy puzzle.

Hidden Single example: Hidden Single: in box 1, 2 fits only in r1c3.
Real example from a Gooby game. In box 1, 2 fits only in r1c3.patterncandidates removeddigit placed

Naked Single Easy

Look at one cell instead of one digit. If its row, column and box already contain eight different digits, only one candidate is left, so that's the answer. The shaded cells below are the peers that rule out the other eight digits.

Naked Single example: Naked Single: r4c3 can only be 9; every other digit is already in its row, column or box.
Real example from a Gooby game. R4c3 can only be 9; every other digit is already in its row, column or box.patterncandidates removeddigit placed

Intersections — where boxes meet lines

Pointing Medium

If, inside a box, a digit's candidates all lie in one row (or one column), then that digit must be placed in that row within this box. So it can't appear anywhere else in the row — remove it from the rest of the row outside the box. Also called a pointing pair or locked candidates, type 1.

Pointing example: Pointing: in box 2, 9 must be in row 2, so 9 is removed from the rest of row 2.
Real example from a Gooby game. In box 2, 9 must be in row 2, so 9 is removed from the rest of row 2.patterncandidates removeddigit placed

Box/Line Reduction Medium

The reverse of pointing. If, inside a row (or column), a digit's candidates all lie in one box, that box must use its copy of the digit on this line. Remove the digit from the other cells of the box. Also called claiming or locked candidates, type 2.

Box/Line Reduction example: Box/Line Reduction: in column 8, 2 only fits inside box 6, so 2 is removed from the rest of that box.
Real example from a Gooby game. In column 8, 2 only fits inside box 6, so 2 is removed from the rest of that box.patterncandidates removeddigit placed

Subsets — pairs, triples and quads

Naked Pair Medium

Two cells in the same unit that have exactly the same two candidates, say {4, 6}. One of them will be 4 and the other 6 — we don't know which yet, but those two digits are used up. Remove 4 and 6 from every other cell of that unit.

Naked Pair example: Naked Pair: in column 4, cells r3c4, r6c4 can only hold {4, 6}, so those digits are removed from the other cells of the column.
Real example from a Gooby game. In column 4, cells r3c4, r6c4 can only hold {4, 6}, so those digits are removed from the other cells of the column.patterncandidates removeddigit placed

Hidden Pair Hard

Two digits that, within a unit, appear as candidates in only the same two cells. Those cells must hold those two digits, so every other candidate in the two cells can go. It's "hidden" because the cells still show extra candidates until you remove them.

Hidden Pair example: Hidden Pair: in box 3, digits {5, 9} fit only in r1c7, r2c9, so other candidates are removed from those cells.
Real example from a Gooby game. In box 3, digits {5, 9} fit only in r1c7, r2c9, so other candidates are removed from those cells.patterncandidates removeddigit placed

Naked Triple Hard

Three cells in a unit whose candidates, together, contain only three digits. Each cell doesn't need all three: {6, 7}, {7, 8} and {6, 8} is a naked triple too. The three digits are locked into those cells, so remove them from the rest of the unit.

Naked Triple example: Naked Triple: in column 1, cells r1c1, r2c1, r7c1 can only hold {6, 7, 8}, so those digits are removed from the other cells of the column.
Real example from a Gooby game. In column 1, cells r1c1, r2c1, r7c1 can only hold {6, 7, 8}, so those digits are removed from the other cells of the column.patterncandidates removeddigit placed

Hidden Triple Hard

Three digits that, within a unit, appear in only three cells. Those cells must hold exactly those digits, so clear every other candidate from them.

Hidden Triple example: Hidden Triple: in box 7, digits {4, 5, 6} fit only in r8c1, r8c3, r9c1, so other candidates are removed from those cells.
Real example from a Gooby game. In box 7, digits {4, 5, 6} fit only in r8c1, r8c3, r9c1, so other candidates are removed from those cells.patterncandidates removeddigit placed

Naked & Hidden Quads Expert

The same idea with four: four cells limited to four digits (naked), or four digits limited to four cells (hidden). They're rare and hard to spot — a useful trick is that if a unit has a naked quad, the remaining empty cells of that unit often form a simpler hidden subset.

Fish — X-Wing and Swordfish

X-Wing Expert

Take one digit. If in two columns that digit can only go in the same two rows, the four cells form a rectangle. The digit must sit in two opposite corners — either way, both of those rows get their copy from these columns. Remove the digit from the rest of both rows. (It works the same with rows and columns swapped.)

X-Wing example: X-Wing: in columns 2 and 9, 2 is confined to the same 2 rows, so 2 is removed from those rows elsewhere.
Real example from a Gooby game. In columns 2 and 9, 2 is confined to the same 2 rows, so 2 is removed from those rows elsewhere.patterncandidates removeddigit placed

Swordfish Master

An X-Wing with three lines. If in three columns a digit's candidates all fall within the same three rows (each column may have only two of them), then those three rows are covered by these columns. Remove the digit from the other cells of those three rows.

Swordfish example: Swordfish: in columns 1 and 6 and 7, 9 is confined to the same 3 rows, so 9 is removed from those rows elsewhere.
Real example from a Gooby game. In columns 1 and 6 and 7, 9 is confined to the same 3 rows, so 9 is removed from those rows elsewhere.patterncandidates removeddigit placed

Wings — chains of two-candidate cells

XY-Wing Expert

Find a pivot cell with two candidates {X, Y}. It sees two wing cells: one with {X, Z} and one with {Y, Z}. If the pivot is X, the first wing is Z; if it's Y, the second wing is Z. Either way one wing is Z, so any cell that sees both wings can't be Z.

XY-Wing example: XY-Wing: pivot r5c3 {6, 9} with wings r5c7 and r6c2 means one wing must be 5, so 5 is removed from cells seeing both wings.
Real example from a Gooby game. Pivot r5c3 {6, 9} with wings r5c7 and r6c2 means one wing must be 5, so 5 is removed from cells seeing both wings.patterncandidates removeddigit placed

XYZ-Wing Master

Like an XY-Wing, but the pivot has three candidates {X, Y, Z} and the wings are {X, Z} and {Y, Z}. One of the three cells must be Z, so Z can be removed only from cells that see all three — the pivot and both wings — which usually means cells in the pivot's box.

XYZ-Wing example: XYZ-Wing: pivot r9c6 {1, 4, 5} with wings r3c6 and r9c5 forces 5 into one of the three, so 5 is removed from cells seeing all of them.
Real example from a Gooby game. Pivot r9c6 {1, 4, 5} with wings r3c6 and r9c5 forces 5 into one of the three, so 5 is removed from cells seeing all of them.patterncandidates removeddigit placed

Practise with hints that teach

In the app, a hint highlights the cells and names the technique from this guide before it fills anything in. Free, offline and ad-free.

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