Rationals Between

What fractions can you find between the square roots of 56 and 58?

Root to Poly

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

Consecutive Squares

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

Napier's Location Arithmetic

Stage: 4 Challenge Level:

Part One : Work systematically - look at $1$ multiplying something, then at $2$ multiplying the same number, then $3, 4$ and so on.

Part Two : If this wasn't possible to do, how could you show that it was impossible?

Part Three : Start with a smaller version of the same kind of grid, perhaps having only $1, 2$ and $4$ with which to make each factor.