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Be Reasonable

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

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Good Approximations

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

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Rational Roots

Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.

Road Maker 2

Age 16 to 18 Short Challenge Level:




You might like to consider working out the destinations of these paths. It is helpful to move along each path one tile at a time and record the coordinates of one of the vertices as you go.