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Be Reasonable

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

Good Approximations

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

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.