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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 eight jars 1 to 8. Take pill/s from the jars according to their label. Take one pill from jar 1, two pills from jar 2, …, and eight pills from jar 8. Weigh all pills (36 pills) taken from the jars. To get the number of jar that has contaminated pills, subtract the measured weight to the total weight when all pills are medicine. Suppose jar 3 has contaminated pills, 36(1000) - 1(1000) - 2(1000) - 3(999) - 4(1000) - 5(1000) - 6(1000) - 7(1000) - 8(1000) = 36000 - 1000 - 2000 - 2997 - 3000 - 4000 - 5000 - 6000 - 7000 - 8000 = 36000 - 35997 = 3. The other jars will have medicine pills.

2. Label the eight jars 1, 10000, 100000000, …, 10000000000000000000000000000. Add four zeroes on the label of the next jar. The same as number 1, take pill/s from the jars according to their label. To get the label of jar/s that has contaminated pills, subtract the measured weight to the total weight when all pills are medicine. Suppose jars with label 1 and 10000 have contaminated pills, 10001000100010001000100010001(1000) - 10000000000000000000000000000(1000) - 1000000000000000000000000(1000) - 100000000000000000000(1000) - 10000000000000000(1000) - 1000000000000(1000) - 100000000(1000) - 10000(999) - 1(999) = 10001000100010001000100010001000 - 10001000100010001000100009990999 = 10001. The answer indicates that jar 10000 + jar 1 have contaminated pills.

• Thanks Mark,

I have sent you my comment via email.

Concerning question 2: please keep in mind each jar can contain hundreds of pills, but  the pills are all good emdecine or all contaminated (thus no mix in one same jar)