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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. Place one pill of jar #1, two pills of jar #2, three pills of jar #3 ... and 8 pills of jar #8 onto the scale.
        If the reading shows:
        xxxx2 mg, then jar #8 is the one with the contaminated pills
        xxxx3 mg, then jar #7 is the one with the contaminated pills
        .....
        xxxx9 mg, then jar #1 is the one with the contaminated pills

    2. Place one pill of jar #1, two pills of jar #2, four pills of jar #3 ... and 128 pills of jar #8 onto the scale.
        If all pills are not contaminated you will read 255'000 mg.
        If there are any contaminated pills, you will read "x" mg less than 255'000 mg
        Convert "x" to binary. Every "1" in the binary number indicates a jar with contaminated pills,
         the LSB corresponds to jar #1 ... the MSB corresponds to jar #8

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  • 1. Place one pill of jar #1, two pills of jar #2, three pills of jar #3 ... and 8 pills of jar #8 onto the scale.
        If the reading shows:
        xxxx2 mg, then jar #8 is the one with the contaminated pills
        xxxx3 mg, then jar #7 is the one with the contaminated pills
        .....
        xxxx9 mg, then jar #1 is the one with the contaminated pills

    2. Place one pill of jar #1, two pills of jar #2, four pills of jar #3 ... and 128 pills of jar #8 onto the scale.
        If all pills are not contaminated you will read 255'000 mg.
        If there are any contaminated pills, you will read "x" mg less than 255'000 mg
        Convert "x" to binary. Every "1" in the binary number indicates a jar with contaminated pills,
         the LSB corresponds to jar #1 ... the MSB corresponds to jar #8

Children