Killer Sudoku

Killer Sudoku (also known as Sumoku, Sum Doku, or Samunamupure) is a puzzle that combines elements of Sudoku and Kakuro. Despite the intimidating name, many players find it easier than regular Sudoku once they learn the basic arithmetic strategies.

The Rules

Killer Sudoku follows all the standard rules of regular Sudoku (1-9 in every row, column, and 3x3 box). However, it introduces one major twist:

• The grid is covered in dotted outlines called cages.
• Each cage contains a small number in the top-left corner.
• The numbers placed inside the cage must add up exactly to that target number.
• Numbers cannot repeat within a single cage.

The Rule of 45

The most important mathematical secret to Killer Sudoku is the "Rule of 45". Because every row, column, and 3x3 box must contain the digits 1 through 9 exactly once, the sum of any complete row, column, or box is always exactly 45 (1+2+3+4+5+6+7+8+9 = 45).

You can use this to your advantage. If a 3x3 box is entirely filled by cages, except for one single cell hanging outside the cages, you can calculate the exact value of that outside cell by adding up the cages and subtracting from 45!