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SudokuIQ#4 [s = (x + n) mod 9, with 0 → 9]
x = Sudoku digit from 1 to 9 n = Number of the 3×3 square (see diagram next to the board) s = (x + n) mod 9 If s = 0, then s = 9 |
How to Play SudokuIQ #4
[s = (x + n) mod 9, with the rule: if s = 0, write 9]
The digits from 1 to 9 are encrypted according to the key:
s = (x + n) mod 9, with the rule: if s = 0, write 9
Where:
x – a digit from classic Sudoku
n – the number of the 3×3 square (see the diagram next to the board)
s – the encrypted number
How to decrypt a number from the board?
If you see 9, treat it as 0 in the cipher.
Subtract the number of the 3×3 square (n) from it.
If the result is less than or equal to 0, add 9.
You will get the original Sudoku digit (x).
Example – Decryption:
The cell contains 5, located in square no. 8.
5 − 8 = −3
Add 9 → 6
Original digit: 6
How to encrypt?
Add the Sudoku digit (x) to the number of the 3×3 square (n).
Divide the sum by 9 and keep only the remainder (mod 9).
If the remainder is 0, write 9 on the board.
Example – Encryption:
You want to encrypt digit 4 located in square no. 5.
4 + 5 = 9
9 mod 9 = 0
If the result is 0 → write 9 on the board.
Answer:
The encrypted digit on the board is 9.
Another example:
Encrypt digit 7 in square no. 3.
7 + 3 = 10
10 mod 9 = 1
The result is 1, so you write 1.
Your goal:
Fill the entire Sudoku board so that, after decrypting all cells, each row, column, and 3×3 square contains all digits from 1 to 9 – according to the rules of classic Sudoku.
The diagram next to the board shows the numbering of the 3×3 squares.
Modulo 9 with Zero Replaced by Nine – Applications and Fun Facts
Modulo 9 (the remainder after division by 9) is a popular mathematical operation widely used in encryption, puzzles, and various logic games such as SudokuIQ. In practice, you will often encounter the notation „mod 9, with 0 → 9”, meaning that any remainder equal to zero is replaced with nine. This method makes it easier to create codes and interesting number puzzles.
In online Sudoku, you can also find similar mechanisms – for example, try the game with Modulo 10 available here: Sudoku Online – IQ #4/3.
This is a great opportunity to explore the practical applications of the modulo operation in everyday puzzles!