The solutions to both parts of the problem were explained very well by Robert Nield (Age 9, Moorgate C P School, Staffordshire), Jack Fawthrop (Age 9) & Jesse Allen (Age 10, Tattingstone School), Daniel Loh (Age 10, Anglo-Chinese School, Singapore), Samantha Poh, Julie (The Abbey) and Ashley.

This solution to the 4 bar problem is from Laura Plant (Age 9, 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 Anderton, Sarah Peake & Ellie Jefferson(Age 11/12, 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.