jmc

Let $a$ be the number of pennies that Alex currently has, and let $b$ be the number of pennies that Bob currently has. If Alex gives Bob a penny, Alex will have $a-1$ pennies and Bob will have $b+1$ pennies. Also, Bob will have three times as many pennies as Alex has, so $b+1=3(a-1)=3a-3$. If Bob gives Alex a penny, Alex will have $a+1$ pennies and Bob will have $b-1$ pennies. Also, Bob will have twice as many pennies as Alex has, so $b-1=2(a+1)=2a+2$.

If we subtract the second equation from the first, we obtain $2=a-5$, so $a=7$. Plugging this in, we can find that $b=17$, so Bob has $\boxed{17}$ pennies.