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Home / General Aptitude / Puzzles / Sudoku
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Sudoku

Sudoku, number, letter, logic, card and clock puzzles.

About Sudoku

A sudoku puzzle is a nine by nine grid to be filled so that every row, every column and every three by three block contains the digits one to nine, each exactly once. The rule is short and the grid does the rest: a digit belongs in a cell only when nothing in the same row, column or block already uses it.

What you need to understand

  • Every row, every column and every three by three block contains the digits 1 to 9, once each.
  • A cell is decided by all three groups together. If eight of the nine digits already appear in one of them, the ninth is forced.
  • Scanning comes first: run your eye along each row and each block to see which digits are missing.
  • A digit missing from a row is easy to spot when that row has only one empty cell.
  • A block hides a digit just as a row does, so check all three groups before deciding a cell is difficult.
  • When a cell cannot be decided at once, note its possible digits in the margin rather than guessing.
  • A digit is ruled out only by the same row, the same column or the same block, not by its use elsewhere in the grid.

How to work through these questions

  1. Look for a line or block that already holds eight different digits. The last cell takes the one that is missing.
  2. Work through the rows first, then the columns, then the blocks.
  3. Write down the digits already present in the row and the column of the cell you are deciding.
  4. Strike those digits out of 1 to 9. The one left is the value of the cell.
  5. Check the block separately, because it can rule out a digit that the row and column both allow.
  6. Read the question again to be sure which cell is being asked about.

Mistakes that cost marks

  • Reading the row and forgetting the column, when both constrain the cell.
  • Forgetting that each block also uses every digit exactly once.
  • Overlooking a digit that already appears in the line being filled.
  • Answering for the wrong cell when more than one is empty.
  • Writing a digit that repeats one in the same block, because only the row and column were checked.
  • Deciding a digit is impossible because it was used somewhere else in the grid, rather than in the same row, column or block.

Worked example

A finished sudoku has one row removed, leaving the cell in row 3, column 3 empty. Which digit belongs in that cell?
  1. The column holding the cell is complete apart from this cell, so begin by listing the digits that column already contains.
  2. Suppose the column holds 2, 3, 4, 5, 6, 7, 8 and 9.
  3. That is eight of the nine digits, so the only one missing from the column is 1.
  4. The cell must therefore hold 1, because a column contains each digit exactly once.
Answer: 1

Practice questions with answers

A few Sudoku questions with the full solution shown, so you can see how the method is applied before you attempt the timed set.

Question 1
One row of this completed sudoku has been left out.
325746918476198352968457231732681495514923876183564729659372184247819563
Which digit belongs in row 3, column 3?
  • A 3
  • B 4
  • C 2
  • D 1
Answer: Option D — with explanation
Only one row of the grid is blank, so every other line is complete. The column containing this cell already holds 2, 3, 4, 5, 6, 7, 8, 9, which is eight of the nine digits. The digit missing from it is 1, and that is the value the cell must take. Common mistakes - read the digit missing from a different line of the grid: 3 - read the digit missing from a different line of the grid: 4 - read the digit missing from a different line of the grid: 2
Question 2
One column of this completed sudoku has been left out.
642378597951268431845926829763155318426746759132973285411569347828461793
Which digit belongs in row 1, column 7?
  • A 3
  • B 1
  • C 2
  • D 4
Answer: Option B — with explanation
Only one column of the grid is blank, so every other line is complete. The row containing this cell already holds 2, 3, 4, 5, 6, 7, 8, 9, which is eight of the nine digits. The digit missing from it is 1, and that is the value the cell must take. Common mistakes - read the digit missing from a different line of the grid: 4 - read the digit missing from a different line of the grid: 2 - read the digit missing from a different line of the grid: 3
Question 3
The grid below is a finished sudoku with one row removed.
895274361671395824432816597346789152527431689253148976789623415164957238
What digit should be written in row 6, column 4?
  • A 8
  • B 6
  • C 5
  • D 7
Answer: Option C — with explanation
Only one row of the grid is blank, so every other line is complete. The column containing this cell already holds 1, 2, 3, 4, 6, 7, 8, 9, which is eight of the nine digits. The digit missing from it is 5, and that is the value the cell must take. Common mistakes - read the digit missing from a different line of the grid: 8 - read the digit missing from a different line of the grid: 7 - read the digit missing from a different line of the grid: 6
Question 4
The grid below is a finished sudoku with one column removed.
628593143874296545631782573146989328657181975243291684577459312616427839
What digit should be written in row 9, column 3?
  • A 6
  • B 5
  • C 8
  • D 7
Answer: Option B — with explanation
Only one column of the grid is blank, so every other line is complete. The row containing this cell already holds 1, 2, 3, 4, 6, 7, 8, 9, which is eight of the nine digits. The digit missing from it is 5, and that is the value the cell must take. Common mistakes - read the digit missing from a different line of the grid: 8 - read the digit missing from a different line of the grid: 6 - read the digit missing from a different line of the grid: 7
Question 5
One row of this completed sudoku has been left out.
586297314739148256241536897127359648394682571965871432873425169412963785
Which digit belongs in row 6, column 9?
  • A 3
  • B 5
  • C 4
  • D 6
Answer: Option A — with explanation
Only one row of the grid is blank, so every other line is complete. The column containing this cell already holds 1, 2, 4, 5, 6, 7, 8, 9, which is eight of the nine digits. The digit missing from it is 3, and that is the value the cell must take. Common mistakes - read the digit missing from a different line of the grid: 5 - read the digit missing from a different line of the grid: 4 - read the digit missing from a different line of the grid: 6

Frequently asked questions

What is the rule of sudoku in one sentence?

Every row, every column and every three by three block must contain the digits one to nine, each exactly once.

How do I fill a cell when several digits seem possible?

Compare the row, the column and the block containing that cell. A digit is possible only if none of the three already uses it, and often just one survives.

Is it enough to check the row?

No. The column and the block constrain the cell just as much, and a digit the row allows can still be ruled out by either of the others.

What if a line has more than one empty cell?

Then that line alone decides nothing. Look for a line or block with a single empty cell, or narrow the possibilities until only one remains.

Do I ever need to guess?

A well-formed sudoku never requires guessing. If you find yourself guessing, a digit has been placed wrongly earlier, so check the work so far.

Take the Sudoku test

Two timed papers on the same syllabus — sit the foundation paper first, then the advanced one. Both use the real exam paper format with a full step-by-step review of every question once you submit.

Set 01 • Foundation Level
Sudoku — Foundation Paper
25 Questions
30 Minutes
+2 / −0.5 Marking
Start this paper
Set 02 • Advanced Level
Sudoku — Advanced Paper
25 Questions
30 Minutes
+2 / −0.5 Marking
Start this paper

Free · login required to attempt the timed test

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