Difficult quantity theory of money question Suppose that you live on an island with 100 units of currency. The cultural beliefs of the islanders discourage an excess focus on commerce, which has created two important rules of commerce. First, you are legally permitted to do 10 transactions per year. Second, the maximum permitted value of each transaction is $10, expressed in USD.

With these assumptions, can you solve for the maximum legal FX rate of the islander's currency expressed in US dollars? I feel like you should be able to do this with some kind of simple, recursive calculation, but for some reason I just can't figure it out right now. GDP is obviously $100 USD per islander and I feel like you can know velocity by knowing the number of transactions per year, but I am not sure how.
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?