All-variables Sudoku

The challenge is to find the values of the variables if you are to solve this Sudoku.

Age
11 to 18
Challenge level
filled star empty star empty star

Thinking mathematically

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Explaining, convincing and proving

Mathematical mindsets

Being curious Being collaborative Being resourceful Being resilient

Problem



By Henry Kwok

 

All-Variables Sudoku



 

Rules of All-Variables Sudoku

Like the standard sudoku, this sudoku variant has three basic rules:

 

  1. Each column, each row and each box (3×3 subgrid) must have the numbers 1 through 9.
  2. No column, row or box can have two squares with the same number.
  3. In addition to the above two basic rules, the puzzle can be solved by finding the values of the 9 given variables in the squares of the 9×9 grid.
At the bottom and right side of the 9×9 grid are groups of similar variables. Each set of variables is the sum of a column or row of variables in the 9×9 grid. A set of 10 equations can be formed from the columns and rows of variables.
For example, in the first and fourth columns beginning from the left of the 9×9 grid, we can form the following equations:
m + n = a
g + n + f = g + c
In the second and last rows beginning from the top of the 9×9 grid, the following equations can be formed:
b + g + f = a + g
e + n + m = a + b + d



 

After solving all the equations, the puzzle is solved by the usual sudoku technique and strategy.



 

An Excel file containing a copy of this Sudoku can be downloaded from the problem notes .