Math 131

Spring 2000

This is due Friday, March 24 at the beginning of class. It is worth 10 points. Papers turned in before class on Monday lose 3 points; papers will not be accepted after Monday. Write neatly or use a word-processor. Your grade will depend on the correctness of your work and how well you explain it. You may discuss your work with me but not with others in the class.

This is a version of exercise 34 on the check digit handout you received.

Determine which transposition errors of the form d₁ d₂ d₃ d₄ d₅ d₆ d₇ d₈ ® d₁ d₂ d₃ d₄ d₆ d₅ d₇ d₈

are detected by the U.P.S. check digit.

Your answer should be a Theorem stating exactly the conditions under which the check digit detects the error (or, alternatively, conditions under which the check digit is not detected) followed by a proof of the Theorem.