Number - March 2007, Stage 4&5

Problems

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Route to Infinity

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you describe this route to infinity? Where will the arrows take you next?

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Twizzles Venture Forth

Stage: 4 Challenge Level: Challenge Level:1

Where we follow twizzles to places that no number has been before.

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Twizzle Arithmetic

Stage: 4 Challenge Level: Challenge Level:1

Arrow arithmetic, but with a twist.

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Twizzle Wind Up

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

A loopy exploration of z^2+1=0 (z squared plus one) with an eye on winding numbers. Try not to get dizzy!

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Twizzle Twists

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

Make the twizzle twist on its spot and so work out the hidden link.

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Elevens

Stage: 5 Challenge Level: Challenge Level:1

Add powers of 3 and powers of 7 and get multiples of 11.

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Tens

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

When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?

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Bina-ring

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

Investigate powers of numbers of the form (1 + sqrt 2).