MathDB

Consider the string of length

6

composed of three characters

a, b, c

. For each string, if two

a

s are next to each other, or two

b

s are next to each other, then replace

aa

b

, and replace

bb

a

. Also, if

a

and

b

are next to each other, or two

c

s are next to each other, remove all two of them (i.e. delete

ab, ba, cc

). Determine the number of strings that can be reduced to

c

, the string of length

1

, by the reducing processes mentioned above.

Problem Statement