Sudoku for beginners: naked singles, hidden singles and notes

Most easy puzzles can be finished with two ideas: a cell that has only one possible digit, and a digit that has only one possible place. This guide shows both on one real puzzle, then how pencil notes keep track of what is still possible.

Written and maintained by Desert Game Studio. The boards and puzzles are our own, and an automated test in our code checks each diagram against the game itself. Last updated .

The practice puzzle and how to name cells

Every example uses the same easy puzzle, made by our own puzzle generator, and it has exactly one solution. Cells are written as R and C with the row first, counted from the top, then the column, counted from the left. R1C1 is the top-left cell and R9C9 the bottom-right. The thicker lines mark the nine three-by-three boxes. The rule is the usual one: each row, column and box holds 1 to 9 once.

A cell's candidates are the digits that could still go in it: those not already in its row, column or box. Both techniques below are just ways of reading candidates.

Naked single: a cell with one candidate

Look at R1C1, the top-left cell. Row 1 already holds 1, 3, 5, 6, 7, 8 and 9, so the cell can only be a 2 or a 4. Column 1 holds a 4 in R7C1 (circled), which removes the 4. Only 2 is left, so R1C1 is a 2.

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Row 1 and column 1 are shaded. The circled 4 in R7C1 rules out a 4 in R1C1, and the row already has every other digit except 2.

This is the first thing to look for in any puzzle. Cells in rows, columns or boxes that are nearly full are the best places to check.

Hidden single: a digit with one place to go

Sometimes a cell has several candidates, but one digit has nowhere else to go in its row, column or box. That digit is a hidden single. Pick a digit, then ask where it can still fit in the unit you are reading.

In a box

Take the top-middle box (rows 1 to 3, columns 4 to 6). It has four empty cells: R2C5, R2C6, R3C5 and R3C6. Where can a 5 go? Row 3 already has a 5 in R3C1, which rules out R3C5 and R3C6. Column 6 already has a 5 in R5C6, which rules out R2C6. That leaves R2C5. Note that R2C5 could still be 2, 3 or 5 by itself, so a check for one candidate per cell would not find it.

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The box is shaded. The two circled 5s cross out R2C6, R3C5 and R3C6, so the 5 in this box must go in R2C5.

In a row

The same works along a row. Row 9 has five empty cells: R9C1, R9C3, R9C5, R9C7 and R9C9. Where can a 9 go? There is a 9 in R8C1, which rules out R9C1 (same column) and R9C3 (same box). A 9 in R4C5 rules out R9C5, and a 9 in R5C7 rules out R9C7. That leaves R9C9. Again the cell on its own could be 2 or 9, so the row view is what finds it.

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Row 9 is shaded. Three circled 9s cross out the other empty cells, so the 9 in this row must go in R9C9.

A good routine is to take one digit at a time and scan every box, row and column for where it fits. Digits that already appear many times are the easiest to place.

Notes: keep your candidates written down

Notes (pencil marks) are small digits in a cell showing what it could still be. They are not needed for easy puzzles, but they stop you re-working the same cells and show naked singles at a glance. Here are the first cells of row 1 of the practice puzzle. R1C1 starts with the single note 2, and R1C2 with 2 and 4. Once the 2 goes into R1C1, the 2 is struck from R1C2, leaving a single 4, which is the next forced digit.

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Before: R1C1 can only be 2, R1C2 can be 2 or 4.
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After placing the 2 in R1C1: R1C2 now has one note left, 4.

In our game, press N or tap Notes to switch note mode, or hold Shift with a digit. On a touch screen, long-press a digit on the pad. Placing a digit clears that note from every cell it sees, so you do not have to strike notes by hand. The full list of keys is under controls on the Sudoku page.

What to do next

Start a puzzle on Easy and look for naked singles first, then check one digit at a time for hidden singles. The practice puzzle here cannot be loaded into the game, which makes its own puzzles, but each one has a single solution and can be solved by logic. If you get stuck, you have 3 hints per puzzle. When singles stop helping on the harder levels, the techniques listed on the game page, such as pair exclusion, come next. If you enjoy this kind of deduction, Minesweeper uses the same habit of ruling cells out.

Ready to try it? Everything on this page works in the live game.

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