Required Mathematical Intelligence

Chapter 106 True and False Silver Dollars
A merchant has 9 silver dollars, one of which is a lighter counterfeit silver dollar.Can you find the counterfeit silver dollar by weighing only twice on a scale (without French yards)?
[Answer: Divide the silver dollars into three groups first, with 3 coins in each group.For the first time, put the two groups on the two pans of the balance respectively.If the balance is uneven, then the fake silver dollars are in the light group; if the balance is balanced left and right, the fake silver dollars are in the third group at the end.

Weigh the group with fake silver dollars again for the second time. When weighing, you can randomly take 2 pieces and put them in two plates respectively. If the balance is uneven, the fake silver dollar will be the lighter one.If the scales are balanced, the last one will be. ]
(End of this chapter)