Barge Math Competition - Spring Semester

Week 2’s Problem: Lots ‘o Letters

Take the collection of “words” made from the alphabet {a,b,c}. Words may be transformed into other words using the following bidirectional rules:

1. a « ab

2. bc « ba

3. ac « cab

4. aba « ac

5. ab « ba

Example: Start with aabab. Then

aabab = aa(ba)b « aa(bc)b = a(ab)cb « a(a)cb = a(ac)b« a(cab)b

So aabab can be transformed into acabb.

a) Can cbaba be transformed into aca?

b) Can baca be transformed into baa?

How to submit your answer:

Bring your solution to the Math Department office in 230 Pardee, or send it by email to Ethan Berkove at berkovee@lafayette.edu. Problem #2 is due by the end of the day on Friday, February 17.