2 out of 3
Generalise this inequality involving integrals.
2 out of 3
Can you make matrices which will fix one lucky vector and crush another to zero?
2 out of 3
Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?
3 out of 3
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.
3 out of 3
Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.
3 out of 3
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
3 out of 3
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
