wolit@rabbit.UUCP (Jan Wolitzky) (02/29/84)
Let X = the original volume of water in the water glass, Y = the volume remaining in the milk glass after dumping it, and Z = the amount of water transferred in each rinse. The algorithm is: dump the milk glass, add Z units of water from the water glass, dump the mixture, and repeat until you run out of rinse water. After the initial dump, there are Y units of milk in the glass. After the first rinse, there are (Y) * (Y / (Y+Z)) units; after two rinses, (Y) * (Y / (Y+Z)) * (Y / (Y+Z)), etc. You can rinse (X/Z) times before you run out of rinse water, so the total volume remaining when done is (Y) * ((Y / (Y+Z)) ** (X/Z)). Since X, Y, and Z are all positive numbers, with Y and X constant, this expression is minimized when Z is minimized; i.e., when an infinitesimal amount of rinse water is used an infinite number of times. Note that this is equivalent to rinsing with a continuous stream of water (at a rate that allows complete mixing), which may (but probably doesn't) explain the presence of a faucet, rather than a series of buckets, in most kitchen sinks. Jan Wolitzky, AT&T Bell Labs, Murray Hill, NJ