There are a pile of 101 gold coins, one of which is fake. You are given a scale that can only be weighed twice. Are you asked to find out whether the fake gold coin is heavier or lighter than the real gold coin?
The first situation
Divide the coins into 50, 50, 1. Weigh 50 and 50. If they balance, the two piles are genuine coins and the remaining 1 is a counterfeit coin. Then weigh the fake currency and the real currency to draw a conclusion.
The second situation
If it is not balanced, then 1 is the genuine coin, and then determine which pile the counterfeit coin is in. Take the light 1 pile, divide it into 25, 25, and weigh it. If balanced, the counterfeit currency is in another pile, and the counterfeit currency is heavier. If it is not balanced, then the counterfeit coins are in the pile and the counterfeit coins are lighter.