Find the Fake Coin: Weighing Strategy with 27 Coins in 3 Attempts

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SUMMARY

The challenge of identifying a fake coin among 27 coins using a balance scale in only three attempts can be efficiently solved by following a systematic grouping strategy. First, divide the 27 coins into three groups of nine and weigh two of the groups against each other. The lighter group contains the fake coin. Next, take the lighter group and divide it into three groups of three coins, weighing two of these groups. Finally, the lighter group from this weighing will leave you with three coins, from which the fake coin can be easily identified in the last attempt.

PREREQUISITES
  • Understanding of balance scales and their functionality
  • Basic knowledge of grouping and elimination strategies
  • Familiarity with logical reasoning and problem-solving techniques
  • Ability to perform simple arithmetic operations
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  • Research combinatorial problem-solving techniques
  • Explore advanced strategies for optimization in weighing problems
  • Learn about decision trees and their applications in logic puzzles
  • Investigate similar coin-weighing puzzles to enhance problem-solving skills
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This discussion is beneficial for puzzle enthusiasts, mathematicians, educators, and anyone interested in logical reasoning and problem-solving strategies.

Some_Student
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Can someone help me please? This is urgent

I can seem to figure this question out. I'm always left with 4 coins and 1 try.

Using a simple balance, could you (by weighing) find the one fake (lighter) coin in a group of 27 coins. Here's the catch...you may only weigh the coins 3 times. You may not use anything else. How could this be accomplished?

If you can get the answer as fast as possible that would help. Thanks.
 
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I know that someone has already done this but i can't seem to find the answer.
 
1) First make three groups of nine coins. balace two of them.
2) Again make three groups of three.Balance two of them.
3) Now there only three coins left to check out and that's easy. :biggrin:
 

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