Difficult quantity theory of money question
The velocity should just be the amount of times the average unit of currency exchanges hands per year. That is $10$ if we take the highest possible number. 

Money supply is $100$ units of island currency ($IC$), so that the left side of

$$MV=PY $$

turns into $100*10$ Nominal GDP, 
so $YP$, is \$$100$ per Islander, or 
$$\$100/XR*n $$ in $IC$, 
where $XR$ is the exchange rate of $USD/IC$ and $n$ is the amount of people. 

Then we get 
$XR=1/10*n$. 

However, I'm a bit lost for what $n$ would be in this case. I'm guessing you got this far yourself?