Steven has 9 gold coins that are identical in appearance. However, one coin is counterfeit an weighs slightly less that the others. Using a balance scale, how can he find the counterfeit coin in just two weighings?

Answer 1

Split the coins into three groups, A, B and C consisting of 3 coins in each group.

Weigh: A--B
1. If A=B, the the counterfeit is in group C
Weigh any two coins in group C and figure out the rest.

2. If A≠B, then the counterfeit is in the lighter group.
Weigh any two coins in the lighter group and figure out the rest.

Answer 2

what if the counterfeit coin is on the heavier side because it would tip the scales if a normal one was on the lighter side and a normal one plus the counterfeit one was on the heavier side