A chemist prepares four solutions one Friday afternoon, then goes home without labeling them. When she arrives back on Monday she faces the problem of identifying the bottle containing each reagent so she will not have to prepare new ones.
The four solutions are () sodium chloride, () hydrogen chloride, () calcium chloride and () sodium carbonate – unfortunately, they're all colorless liquids. If and are mixed, fizzing will result from the release of carbon dioxide. If and are mixed a white solid (calcium carbonate) will be precipitated. Any other mixture simply produces another colorless liquid.
How is she to proceed? She can do the tests by mixing just a drop or two of each, each time – thus she won't waste much of any of them.
Solution
Since the four solutions are identical in appearance, the chemist simply must try combinations more-or-less at random (there are six possible combinations, right?) until the two mixtures that cause a reaction are identified. When this is accomplished, she will see that is the solution common to those two reactions, so she has found . It will also be obvious which bottles contain and . By elimination, the remaining bottle is .