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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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  • 1) Label the jars 1-8. Pull out a number of pills from each jar equal to the jar number (eg, 3 pills from jar #3).  Weigh all the pulled pills.  The weight should be 36,000mg (36g) if all the pills were OK but the weight will be smaller due to the pills that are contaminated.  The amount of milligrams that the weight is below 36,000mg is the number of the jar that is contaminated (eg, if the weight is less than 36,000g by 4mg, then bottle #4 is the contaminated bottle.)

    2) I assume that each jar has at least 256 pills in them.  So, similar to number one, only this time take a number of pills equal to 2 to the exponent of the bottle number (eg, take 2^4 = 16 pills from jar #4).  Weigh all the pills and the weight reduction due to contaminated pills will be a number corresponding to the bottles that are contaminated.  You must look at the number in its binary form though (it will be an 8 bit number), so if the weight is short by 138mg, then its binary equivalent is 10001010 and therefore bottles 8, 4, and 2 are contaminated.)

    Brian Barrett

  • And yes, as stated in the quiz, each jar contains hundreds of pills; therefore no problem to take 256 pills out of any jar....

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