Contaminated Pills

You have five jars of pills. All the pills in one jar only are “contaminated.” The only way to tell which pills are contaminated is by weight. A regular pill weighs 10 grams; a contaminated pill is 9 grams. You are given a scale and allowed to make just one measurement with it How do you tell which jar is contaminated?

Solution

Solution is to call the bottles #1, #2, #3, #4, and #5. Take one pill from #1, two from #2, three from #3, four from #4, and five from #5. Weigh the whole lot. Were all the pills normal, the result would be 10 + 20 + 30 + 40 + 50 = 150 grams. In fact, the weight must fall short of this by a number of grams equal to the number of the contaminated bottle. Should the total weight be 146 (4 grams short), then bottle #4 must contain the lighter pills.