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Rationals Between

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

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Root to Poly

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

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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: Challenge Level:1

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.