consider the path of length 2 that
starts at the vertex <i>c</i>=5 and has both edges labeled <i>a</i>=<b>t</b>.
Where does it end? (Answer: <i>c</i>=7.)<p>

<i>Postdiction.</i>  I just put one coin in the box twice in a row, and now
there are 5 coins in it.  How many coins were there in the box initially?<p>

In terms of paths: consider the path of length 2 that ends at the vertex
<i>c</i>=5 and has both edges labeled <i>a</i>=<b>t</b>.  Where does it
start?  (Answer: <i>c</i>=3.)<p>

<i>Planning.</i>  Cur