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KCC's Quizzes: Contaminated Pills

  1. Eight jars with hundreds of identical looking pills, although 7 jars have medicine pills of 1000 mg each, 1 jar has contaminated pills of 999 mg each. The contaminated pills are ever so slightly lighter than the medicine pills. You have a precise electronic scale (precision better than 1mg). With ONE (1) weighing, how can you detect the jar with the medicine pills?
  2. Same question as above but the situation is there could be multiple jars with contaminated pills. With ONE (1) weighing, how can you identify which jars (could be multiple) have contaminated pills?

Many thanks to Ralph Montforts, ADI Director, General Accounting for proposing this quiz!

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[edited by: emassa at 3:46 PM (GMT -5) on 18 Jan 2023]
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  • Answer 1. You can take 1 pill from jar nr.1, 2 pills from jar nr. 2, 3 pills from jar nr.3 and so on and weigh all the 36 pills. The difference between 36g and the weighing result will give you the number of contaminated pills.

    Answer 2. Same mechanism as above, but you need to take "power of 2" number of pills: 1 from jar 0, 2 from jar 1, 4 from jar 2, 8 from jar 3 and so on. The difference between 255g and the weighing result will allow you to identify the jars with contaminated pills.  

  • Hi Gaetano, as usual, I have answered you via email

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