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?
The scale in this puzzle gives you an actual weight. In a more normal situation, you'd probably weigh a pill from each jar until you found one that weighed 9 grams. That won't work here, since you've got only one Measurement.
You need to manufacture a situation in which the weight measurement is informative. One 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.
Another solution: An alternate solution, with the arguable virtue of weighing fewer pills, is to weigh 1 + 2 + 3 + 4 pills from the first four bottles only. Then, if the weight is less than 100 grams, the shortfall amount points to the rogue bottle. Should the measurement be 100 grams on the nose, the fifth bottle must be contaminated.