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Two false coins (Posted on 2005-03-25) Difficulty: 3 of 5
You have ten coins, but two are fake, and weigh a little less. How many times do you have to use a two arm scale, in order to pick out the two fakes?

  Submitted by Federico Kereki    
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Solution: (Hide)
There are (10,2)=45 ways to pick the two coins out of the ten. Each use of the scale gives three possible result. Thus, with less than 4 uses, you cannot distinguish among 45 cases. Now, you need an algorithm that does this, to complete the proof, and there are such solutions among the comments...

Extra note: if the fake coins didn't weigh the same, we would have 90 ways to pick the two coins, so the scale would have to be used 5 times. Once again, this is a minimum, and until you find the algorithm, you cannot say it's the actual minimum.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
AnswerK Sengupta2009-01-09 12:41:16
SolutionSolution without knowing if the fakes are equalBrian Smith2005-06-02 21:18:14
hmmmmmmmTaylor2005-04-09 23:41:08
re: Existential doubtjohn2005-04-06 16:53:47
Solutionre: GuessDavid2005-03-28 05:37:24
SolutionGuessDavid2005-03-28 05:33:41
Some ThoughtsExistential doubtFederico Kereki2005-03-27 22:29:30
SolutionEric2005-03-26 18:31:13
Some ThoughtsPossibilityKardo2005-03-26 07:31:28
Solutionre: thoughtspete2005-03-26 05:25:35
Some ThoughtsthoughtsCharlie2005-03-25 20:30:57
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