### Why do this
problem?

An

exercise
in proof by induction or, perhaps more simply, modulus
arithmetic.

### Possible approach

The challenge in the question is to find the neatest and simplest
proof. The class could take up this challenge, perhaps working in
pairs. Then the class could discuss criteria for a good write-up of
a proof and the teacher can add advice. Perhaps the class could
then mark each others work say in groups of four.

### Key questions

How couldwe test that an expression is divisible by 33?

What do we notice for small values of n?

What methods do we know for proving a result for all positive
integers?

### Possible support

See

the article related to this problem