The solutions to both parts of the problem were explained very well by Robert ( Moorgate C P School, Staffordshire), Jack and Jesse ( Tattingstone School), Daniel ( Anglo-Chinese School, Singapore), Samantha , Julie (The Abbey) and Ashley .

This solution to the four bar problem is from Laura ( St Ives School, Haslemere)

My solution to the four bars of gold Find the fake is:
The man weights two bars of gold in either of the scales - one side will be lighter, that will have the fake in it. Split the two bars and weigh it again, the lighter will be the fake.

This answer for the 9 bar problem comes from Caroline , Sarah and Ellie ( The Mount School, York),

1. Place 3 bars on each side. If they balance then the fake is in the other 3. If they don't balance then the fake is in the lighter side.
2. Take the 3 bars which the fake is in and weigh 2 of them against each other. If they balance it's the one left over and if they don't balance it is the lighter one.