<------- g ------- f ------- e ------ d ------ c ------ b ------ A ------- B ------- C ------ D ------- E ------ F ------ G ------>

A particle originates at point A and can move left one point or move right point for any move.

It cannot be stationary for any move.

For two moves, the ways can be diagrammed like this:

ABC

ABA

Abc

AbA

Two of those ways begin and end with the particle at the starting point A.

**Question: For six moves, how many of the ways begin and end with the**

**particle at the starting point A?**