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Inside Outside

Age 14 to 16 Challenge Level:

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The bar balances with a weight of 4 units on one side and weights of 2 units and 3 units on the other.

The 2 is on the inside and the 3 is on the outside. The 3 weight and the 4 weight are exactly the same distance from the pivot, and the 2 weight is half way between the 3 weight and the pivot.

Can you find an arrangement with the 4 staying exactly where it is, balanced again by the 2 and 3, but this time with the 3 on the inside and the 2 on the outside?

There is more than one way to do that, so first find at least two arrangements that work, then try to describe, using algebra, the connection between the 2 and 3 positions.

You can use the lines in the background to help you gauge distances when you are looking for the relationship between the positions of the 2 and 3 unit weights.