You have 20 bottles of pills. 19 bottles have 1.0 gram pills, but one has pills of weight 1.1 grams. Given a scale that provides an exact measurement, how would you find the heavy bottle? You can only use the scale once.
First we must assume that each bottle of pills contains at least \(19\) pills.
Next, label each bottle \(0\) to \(19\) sequentially and remove the same number of pills from that bottle as it was labeled. Keep the pills in separate piles so they can be returned to the bottles later.
Weigh the \(210\) pills once and note the weight. By subtracting \(210\) from the weight, we are left with some remainder which indicates the number of pills that we just weight which are \(.1\) gram heavier. So this remainder divided by \(.1\) produces the label number of the bottle that contains heavier pills.