Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site rabbit.UUCP Path: utzoo!watmath!clyde!burl!ulysses!allegra!alice!rabbit!wolit From: wolit@rabbit.UUCP (Jan Wolitzky) Newsgroups: net.math Subject: Re: Rinsing Puzzle Message-ID: <2554@rabbit.UUCP> Date: Wed, 29-Feb-84 10:14:54 EST Article-I.D.: rabbit.2554 Posted: Wed Feb 29 10:14:54 1984 Date-Received: Fri, 2-Mar-84 07:24:12 EST Organization: AT&T Bell Laboratories, Murray Hill Lines: 20 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