# Symmetry, Substitutions and Surprises In this feature you will be challenged to exploit the symmetries of a range of equations to derive elegant and efficient solutions to problems which, at first sight, might seem very difficult.

The last date for submitting solutions to the live problems is Monday 11th July.

### Simultaneous Equations Sudoku

##### Age 11 to 18Challenge Level
Solve the equations to identify the clue numbers in this Sudoku problem.

### Symmetricality

##### Age 14 to 18Challenge Level
Five equations and five unknowns. Is there an easy way to find the unknown values?

### Always Two

##### Age 14 to 18Challenge Level
Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

### Mega Quadratic Equations

##### Age 16 to 18Challenge Level
What do you get when you raise a quadratic to the power of a quadratic?

### Agile Algebra

##### Age 16 to 18Challenge Level
Observe symmetries and engage the power of substitution to solve complicated equations.

### Overturning Fracsum

##### Age 16 to 18Challenge Level
Can you solve the system of equations to find the values of x, y and z?