Frank Morgan's Math Chat


MAY 3, 2001

The Largest Number

Old Challenge. What is the largest positive number that you can represent with three, distinct standard mathematical symbols, such as 8x9? The smallest?

Answer. Eric Brahinsky found both the large 89!, with over a billion digits, and the small .19 = .000000001. A number of readers found the second place winners: the large 789, with over a hundred million digits, and the small 8-9 = .000000007...

New Challenge. Al Zimmermann reports that:

A few years ago I bought a candy bar at the concession stand in a movie theater. I paid with a $20 bill. My change was a thick wad of bills accompanied by the apology, "Sorry for all the singles, but I only have one Ten left and I want to save it in case I need it later."

Does this make any sense? What is the best strategy for making change at a concession stand?

Copyright 2001, Frank Morgan.

Send answers, comments, and new questions by email to, to be eligible for Flatland and other book awards. Winning answers will appear in the next Math Chat. Math Chat appears on the first and third Thursdays of each month. Prof. Morgan's homepage is at

THE MATH CHAT BOOK, including a $1000 Math Chat Book QUEST, questions and answers, and a list of past challenge winners, is now available from the MAA (800-331-1622).