### Plum Tree

Label this plum tree graph to make it totally magic!

### Magic W

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

### 2-digit Square

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

# Reasonable Algebra

##### Stage: 4 Challenge Level:

This problem invites students to explore the power of reasoning based on algebraic forms.

It is important for students to feel confident with the context and therefore spending time on the problem "Consecutive sums" may be an important starting point. By working on this problem the difficulties with solving for powers of 2 often occurs naturally.

Why are powers of 2 impossible? We are aware of two approaches to explaining this:
• one is using an argument based on the diagram offered in the hints and the relationship of the rectangle with odd and even numbers.
• the other involves examination of an algebaric expression that represents the sum - this links with the arguments offered in the solution to the problem "Make 24".
But of course there might be some neater explanations.

The problem Sequences and Series has an interactivity you might wish to use.