Mathematics Problem of the Week
Fall 2004
A number is called self-defined if the first digit from the left indicates the number
of zeros in the number; the second digit indicates the number of ones, and so on.
For example, 42101000 is
self-defined.
1) Find the smallest self-defined number.
2) Is the set of self-defined numbers finite? Why?
3) If the set is finite, how many self-defined
numbers are there? What’s the largest one?
Solutions
should be submitted to Dr. Maegan Bos’ mailbox in the Math office or sent via
e-mail to mbos@stlawu.edu
Presentation counts! The prize-winning entry will be
selected from all correct submissions, based on the clarity, creativity and
elegance of the solution.
Look
for the SLU POW on the Web at http://it.stlawu.edu/~math/activities/