Toughnuts

Try these unsolved problems

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Back Fitter

Stage: 4 Challenge Level: Challenge Level:1

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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The Invertible Trefoil

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

When is a knot invertible ?

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Distribution Differences

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?

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Take a Square II

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What fractions can you divide the diagonal of a square into by simple folding?

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Pythagoras Proofs

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make sense of these three proofs of Pythagoras' Theorem?

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Summing Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

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Pentagon

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the vertices of a pentagon given the midpoints of its sides.

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Bicentric Quadrilaterals

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

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Modular Knights

Stage: 5 Challenge Level: Challenge Level:1

Try to move the knight to visit each square once and return to the starting point. Move either 2 steps one way and one perpendicular (as in chess) or generalise to a steps one way and b the other.

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Into the Exponential Distribution

Stage: 5 Challenge Level: Challenge Level:1

Get into the exponential distribution through an exploration of its pdf.

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What's Your Mean?

Stage: 5 Challenge Level: Challenge Level:1

Can you work out the means of these distributions using numerical methods?

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Classical Means

Stage: 5 Short Challenge Level: Challenge Level:1

Use the diagram to investigate the classical Pythagorean means.

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More Bridge Building

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Which parts of these framework bridges are in tension and which parts are in compression?

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PCDF

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When can a pdf and a cdf coincide?

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Into the Normal Distribution

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Investigate the normal distribution

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Random Inequalities

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you build a distribution with the maximum theoretical spread?

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Pattern Recognition

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

When does a pattern start to exhibit structure? Can you crack the code used by the computer?