Mathematics Problem Of the Week

Spring 2008

POW #6

Indivisible Words

Say that a word like mathematics is divisible by a number n if there is a way to substitute digits for each of the letters of the word (a different digit for each distinct letter) to produce a number that is divisible by n.

For example, mathematics is divisible by 5 since a substitution can make 12346123805.

It should be obvious that any word of ten letters of less is divisible by 5 or 2, but what about 3?

Prove or disprove: Every word with ten or fewer letters is divisible by 3.

Due Friday, March 7^th at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math/CS/Stat office or sent via e-mail to rlock@stlawu.edu.