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# Simultaneous Equations Sudoku

#### Rules of Equation Sudoku

You might like to start by considering the $4^{\text {th}}$ row and $4^{\text {th}}$ column.

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### Real(ly) Numbers

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Age 11 to 18

Challenge Level

by Henry Kwok

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

- Each column, each row and each box (3x3 subgrid) must have the numbers 1 through 9.
- No column, row or box can have two squares with the same number.
- The puzzle can be solved by finding the values of the 9 given variables in the squares of the 9x9 grid. At the bottom and right side of the 9x9 grid are numbers, each of which is the sum of a column or row of variables. Altogether a set of 16 equations can be formed from the columns and rows of variables and constants.

For example, in the first column beginning from the left of the 9x9 grid, we can form the following equation:

$$c + g + k = 17$$

In the fourth row beginning from the top of the 9x9 grid, the following equation can be formed:

$$k + g + m + c = 23$$

If you are not sure where to begin, you can reveal a hint by clicking the button below:

You might like to start by considering the $4^{\text {th}}$ row and $4^{\text {th}}$ column.

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

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?