Finding the Fake Coin in 3 Weightings

  • Context: Undergrad 
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SUMMARY

The discussion centers on the classic problem of identifying a single fake coin among 12 coins using a pan scale within three weighings. Participants emphasize the importance of understanding the problem's constraints and suggest starting with a simpler version involving three coins in two weighings. The problem is historically significant, having been notably explored during World War II, particularly at Bletchley Park. Engaging with this problem enhances logical reasoning and problem-solving skills.

PREREQUISITES
  • Understanding of basic combinatorial logic
  • Familiarity with the mechanics of a pan scale
  • Knowledge of problem-solving strategies in mathematics
  • Ability to analyze and break down complex problems into simpler components
NEXT STEPS
  • Research the "12 Coin Problem" and its historical context
  • Practice solving simpler variations of the problem, such as the "3 Coin Problem"
  • Explore combinatorial game theory techniques
  • Learn about logical deduction methods in mathematical puzzles
USEFUL FOR

Mathematicians, puzzle enthusiasts, educators, and anyone interested in enhancing their logical reasoning and problem-solving abilities.

didi
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Hi,
I have the following to solve and I tried so many things but it is confusing. Here is the problem
Given 12 coins such that exactly one of them is fake (we don't know if it is heavier or lighter than the rest), and a pan scale, devise a procedure to identify the fake coin and whether it is heavier or lighter by doing no more than 3 weightings.

Thank you :smile:
didi
 
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A very famous problem that is alleged to have caused many problems with people at some important mathematical institution during WW2 (bletchley?) as they spent too much time trying to solve it. I'm sure that if you really don't want to spend time proving it the answer is googlable. But you really ought to try it and at least post your musings here. Though undoubtedly some one will sadly post the solution for you.
 
Try solving it with 3 coins in 2 tries first
 

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