# Number - March 2007, Stage 4&5

## Problems

### Route to Infinity

##### Stage: 3 and 4 Challenge Level:

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

### 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).