Explaining, convincing and proving

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?

There are many different methods to solve this geometrical problem - how many can you find?

Can you find a way to prove the trig identities using a diagram?

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Can you invert the logic to prove these statements?

Can you work through these direct proofs, using our interactive proof sorters?

Was it possible that this dangerous driving penalty was issued in error?

Do you have enough information to work out the area of the shaded quadrilateral?

If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?

By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn