The three glass puzzle asks if it is possible to produce exactly four ounces of a liquid if given a full eight ounce glass and two empty three and five ounce glasses. The author provides a simulation of the pouring from one glass into another and discusses connections to number theory, graph theory and barycentric coordinates. Variations of the puzzle and the general solution are discussed also.
Type of Material:
This applet should run on any platform.
Identify Major Learning Goals:
A demonstration of the applicability of several branches of mathematics in the solution of puzzles.
Target Student Population:
General audiences can understand the puzzle. Parts could be used as an enrichment activity in a good high school class or in general mathematics classes.
Prerequisite Knowledge or Skills:
The problem is discussed thoroughly in the applet and references are given. Ideas are presented clearly and the graphics are helpful. The general solution is also provided. The puzzle has been proven to have a solution for any desired quantity not exceeding the capacity of the large glass provided the capacities of the two small glasses are mutually prime. This is shown on the page http://www.cut-the-knot.com/ctk/Water.html
Potential Effectiveness as a Teaching Tool
The site does an outstanding job of leading the student to look at different solution methods, thus exposing students to topics from graph theory and number theory and leading them to the powerful (but under utilized) method of barycentric coordinates.
It may be worth mentioning the appearance of a puzzle of this type in "Die Hard III - with a vengeance", which may appeal to some people.
Ease of Use for Both Students and Faculty
The applet itself is very easy to use. The user can also explore problems with other glass volumes by using the "define a new problem" applet
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