Error Correcting Codes
4x4 Sudoku Step-by-Step Solution guide
In the Getting the Message Activity participants will be required to complete 4x4 sudoku puzzles.
While the 4x4 sudoku is simpler that the standard 9x9 sudoku, the unfamiliar format may confuse
some people.
This document is to provide a detailed solution of a specific 4x4 sudoku to be used as a worked
example for the Getting the Message Activity.
Please note that each step will state the specific rules being used to fill in a missing number.
The text will seem repetitive but this has been done on purpose to be as thorough as
possible for those unfamiliar with sudoku.
No. Steps
Illustration/Example
1
In the Getting the Message activity, a passcode is
first written in patterned code squares above the
sudoku.
2
Each digit of the passcode is re-written into the
empty 4x4 sudoku by matching the pattern of the
code square to the respective pattern in the grid.
The empty 4x4 sudoku can now be completed
following the same three rules that apply to a
regular 9x9 sudoku, just for less numbers.
The specific rules for a 4x4 sudoku are:
1. The numbers 1 to 4 are placed once in
every row.
2. The numbers 1 to 4 are placed once in
every column.
3. The numbers 1 to 4 are placed once in
every 2x2 box.
Page 1 of 4
© Simon Pampena - free for educational use within Australia
No. Steps
Illustration/Example
3
Starting with the top two rows we see the number
3 in the first row and the number 2 in the second
row. Since sudoku rules say each number can
only appear once in every row means 2 cannot
appear again in the second row BUT sudoku rules
also say each number appears once in every box.
That means in the top left 2x2 box there is only
one possible position for the 2, next to the 3 in the
first row.
4
We can now use the same logic for the 3 in the
first row: sudoku rules say each number can only
appear once in every row means 3 cannot appear
again in the first row BUT sudoku rules also say
each number appears once in every box. That
means in the top right 2x2 box there is only one
possible position for the 3, this time next to the 2 in
the second row.
5
Now if we switch to looking to the two leftmost
columns we see a 3 in the first column and a 4 in
the second column. Sudoku rules say each
number can only appear once in every column
meaning 3 cannot appear again in the first column
BUT sudoku rules also say each number appears
once in every box. That means in the bottom left
2x2 box there is only one possible position for a 3,
below the 4 in the second column.
6
Next we switch to looking to the two rightmost
columns where we see a 2 in the third column and
a 4 in the fourth column. Sudoku rules say each
number can only appear once in every column
meaning 2 cannot appear again in the third
column BUT sudoku rules also say each number
appears once in every box. That means in the
bottom right 2x2 box there is only one possible
position for the 2, above the 4 in the fourth
column.
Page 2 of 4
© Simon Pampena - free for educational use within Australia
No. Steps
Illustration/Example
7
Returning to the leftmost two columns, sudoku
rules say each number can only appear once in
every column meaning 4 cannot appear again in
the second column BUT sudoku rules also say
each number appears once in every box. That
means in the top left 2x2 box there is only one
possible position for the 4, below the 3 in the first
column.
8
Now, looking inside the top left 2x2 box we see
that there is only one space left. Using the sudoku
rule that each number appears once in every box
means there must be only number that can fill in
the missing spot. If the box already contains 2, 3
and 4 means the last remaining digit must be 1.
9
Returning to the two rightmost columns where we
see a 4 in the fourth column. Sudoku rules say
each number can only appear once in every
column meaning 4 cannot appear again in the
fourth column BUT sudoku rules also say each
number appears once in every box. That means in
the top right 2x2 box there is only one possible
position for the 4, above the 2 in the third column.
10
Inside the top right 2x2 box we see that there is
only one space left. Using the sudoku rule that
each number appears once in every box means
there must be only number that can fill in the
missing spot. If the box already contains 2, 3 and
4 means the last remaining digit must be 1.
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© Simon Pampena - free for educational use within Australia
No. Steps
Illustration/Example
11
Looking down at the bottom two rows we see the
number 2 in the third row. Since sudoku rules say
each number can only appear once in every row
means 2 cannot appear again in the third row BUT
sudoku rules also say each number appears once
in every box. That means in the bottom left 2x2
box there is only one possible position for the 2,
next to the 3 in the fourth row.
12
Now, inside the bottom left 2x2 box we see that
there is only one space left. Using the sudoku rule
that each number appears once in every box
means there must be only number that can fill in
the missing spot. If the box already contains 2, 3
and 4 means the last remaining digit must be 1.
13
Returning to the bottom two rows we now have the
number 1 in the third row. Since sudoku rules say
each number can only appear once in every row
means 1 cannot appear again in the third row BUT
sudoku rules also say each number appears once
in every box. That means in the bottom right 2x2
box there is only one possible position for the 1,
next to the 4 in the fourth row.
14
Finally, inside the bottom right 2x2 box we see that
there is only one space left. Using the sudoku rule
that each number appears once in every box
means there must be only number that can fill in
the missing spot. If the box already contains 1, 2
and 4 means the last remaining digit must be 3.
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© Simon Pampena - free for educational use within Australia