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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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Parents
  • Q1: Take 1 pill for jar 1, 2 for jar 2, 3 for jar 3... The difference between measurement and expected weight will give you the contaminated pills jar number.

    Q2: Same logic but combination between jars pills must give a sum that is unique for every combination. Thus, the measurement will give you the only possible combination. One possibility is:

    number of pills _ from jar number

    1 _ 1,

    2 _ 2,

    4 _ 3,

    8 _ 4,

    13 _ 5,

    22 _ 6,

    46 _ 7,

    69 _ 8

Reply
  • Q1: Take 1 pill for jar 1, 2 for jar 2, 3 for jar 3... The difference between measurement and expected weight will give you the contaminated pills jar number.

    Q2: Same logic but combination between jars pills must give a sum that is unique for every combination. Thus, the measurement will give you the only possible combination. One possibility is:

    number of pills _ from jar number

    1 _ 1,

    2 _ 2,

    4 _ 3,

    8 _ 4,

    13 _ 5,

    22 _ 6,

    46 _ 7,

    69 _ 8

Children