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.

Lee, yuour assertion that water volume = ice volume is incorrect.  In fact, ice floats because it has a lesser density than ice.  If it had the same density, it wouldn't float (though it wouldn't sink either...)  As ice has a lesser density, the same amount (say, in moles) of it will occupy a greater volume.

A simple experiment performable in your home to illustrate this.  Take a clear glass, and fill it mostly full with water.  Add some ice (one or two cubes - not enough to create a full layer at the top of the glass), and then fill the remainder of the glass with water until the surface tension is all thats stopping the water from overflowing the edge.  Notice that the ice is floating above the level of the water.  Now wait for the ice to melt...  If the volume of the iced-water stayed the same, wneh it melted, the water would have overflowed - but I'll bet that it didnt!