Number - March 2007, Stage 4&5

Problems

Twizzles Venture Forth

Stage: 4 Challenge Level:

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

Twizzle Arithmetic

Stage: 4 Challenge Level:

Arrow arithmetic, but with a twist.

Twizzle Wind Up

Stage: 4 Challenge Level:

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

Twizzle Twists

Stage: 4 Challenge Level:

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

Elevens

Stage: 5 Challenge Level:

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

Tens

Stage: 5 Challenge Level:

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

Bina-ring

Stage: 5 Challenge Level:

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