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Dr Tan's Math & Logic Problem 003
Counterfeit Coin Puzzle
This is a logic problem. The easier variant is the Nine-coin problem.
Nine coins are identical in weight except one, which is a counterfeit and is lighter than the others.
How can one isolate the counterfeit coin with only two weighings on a two-pan balance?
The harder variant is the Twelve-coin problem.
Twelve coins are identical in weight except one, which is a counterfeit. It has a different weight but we do not know whether it is lighter or heavier than the others.
How can one isolate the counterfeit coin and determine whether it is lighter or heavier with only three weighings on a two-pan balance? If you have succeeded in solving the nine-coin variant which is fairly easy, you can attempt the twelve-coin variant which is quite convoluted.

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Titles 00*
000 Glass Half Full    • Glass Half Full  
001 Truth Teller and Liar    • Truth Teller and Liar  
002 Birthday Problem    • Birthday Problem  
003 Counterfeit Coin Puzzle    • Counterfeit Coin Puzzle  
004 Vietnamese Math Puzzle    • Vietnamese Math Puzzle  
005 Cheryl's Birthday    • Cheryl's Birthday  
006 Monty Hall Problem    • Monty Hall Problem  
007 Handshake Logic Puzzle    • Handshake Logic Puzzle  
008 Ages of Three Children    • Ages of Three Children  
009 Four Knights Puzzle    • Four Knights Puzzle