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Symmetry, Substitutions and Surprises

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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. 

 

 

 

Symmetricality
problem

Symmetricality

Age
14 to 18
Challenge level
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Five equations and five unknowns. Is there an easy way to find the unknown values?
Always Two
problem
Favourite

Always Two

Age
14 to 18
Challenge level
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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
problem

Mega Quadratic Equations

Age
14 to 18
Challenge level
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What do you get when you raise a quadratic to the power of a quadratic?
Agile Algebra
problem

Agile Algebra

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

Overturning fracsum
problem

Overturning fracsum

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