### 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?

# Balance Point

##### Stage: 4 Challenge Level:
Well done to Jim sent us his solution:

The trick to solving this problem is to work systemticlly. The 8 weight can be placed on either the end or the inner point, and it is symetrical so we only have to look at on side.

If the 8 is on the end the arrangements to consider are:
8124
8142
8214
8241
8412
8421

If the 8 is on an inner attachment point we need to consider:
1824
1842
2814
2841
4812
4821

I them tried to find the balance points, and found they were in the central interval except for 8241, 8412 and 8412. I found that 4821 and 8142 produce a balance point at one of the inner attachment points.

For 8241, and 8412 the bar needs weight 4/3, for 8421, 8/3 is required. So the bar must be at least 8/3 in weight for all arrangments to have balance points in the central interval.