Balance of Halves
We've had one way of doing it using a weight on the $\frac{1}{2}$
peg. How could you balance 7 using $1\frac{1}{2}$? Can you carry on
going along the balance like this trying the "half numbers" in
turn?
How will you make a note of what you have done?
How will you know that you have got all the different ways?