### 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:

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Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. The bar strangely has no weight of its own.

Move the bar from side to side until you find a balance point. Is it possible to predict that position
(you might find it helps to look at the problem called "Inside Outside" first)

Which arrangements produce balance points outside the central interval (between the two inner attachment points for weights)?

If the bar now does have weight, what is the least weight it could have with no arrangements that produce balance points outside the central interval.

You only need the 1, 2, 4 and 8 unit weights for the problem set but the others are there to let you explore, conjecture and test - have fun.