My wife and I were cookin' a Cajun feast for the anniversaire de ma mere. While I handled the vittles, the lovely and talented Mrs. Boy made the drinks.
  She had made the tea strong and wanted to dilute it with 4 cups of water but the guests were at the door and the tea was still hot so she decided to dilute it with ice instead.
  She turned to me and said, "Fat, sweetie, how many ice cubes make a cup of water?"
  I confessed that I did not know as I had not measured the water when I made the cubes. To make matters worse I had not paid attention to how full I had made the trays so we couldn't just refill them and see how much they held.
  Things seemed desperate, as I'd die before I'd serve my Gumbo without sweet tea, but Mrs. Boy is no fool and she found a way. The tea was just right (though the cheese grits were a little burnt).

How did Mrs. B manage to ascertain the proper number of ice cubes to produce the 4 cups of water needed to dilute the tea? All she had to use was the ice cubes themselves, an ungraduated glass pitcher of unknown volume and the 4 cup graduated Pyrex measuring cup full of (too strong) tea.

....she knew all about the Archimedes Principle. She took one of the ice cubes, put it in the ungraduated glass pitcher, and measured the amount of fluid that was displaced. (We must assume that she could perform this measurement, since the puzzle states that "To make matters worse I had not paid attention to how full I had made the trays so we couldn't just refill them and see how much they held.")

Archimedes Principle:

The principle that states that a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. The principle applies to both floating and submerged bodies and to all fluids, i.e., liquids and gases. It explains not only the buoyancy of ships and other vessels in water but also the rise of a balloon in the air and the apparent loss of weight of objects underwater. In determining whether a given body will float in a given fluid, both weight and volume must be considered; that is, the relative density, or weight per unit of volume, of the body compared to the fluid determines the buoyant force. If the body is less dense than the fluid, it will float or, in the case of a balloon, it will rise. If the body is denser than the fluid, it will sink. Relative density also determines the proportion of a floating body that will be submerged in a fluid. If the body is two thirds as dense as the fluid, then two thirds of its volume will be submerged, displacing in the process a volume of fluid whose weight is equal to the entire weight of the body. In the case of a submerged body, the apparent weight of the body is equal to its weight in air less the weight of an equal volume of fluid. The fluid most often encountered in applications of Archimedes' principle is water, and the specific gravity of a substance is a convenient measure of its relative density compared to water. In calculating the buoyant force on a body, however, one must also take into account the shape and position of the body. A steel rowboat placed on end into the water will sink because the density of steel is much greater than that of water. However, in its normal, keel-down position, the effective volume of the boat includes all the air inside it, so that its average density is then less than that of water, and as a result it will float.

Edited on March 9, 2004, 8:51 am

Posted by Penny on 2004-03-09 08:42:44