Question 100
Let $n$ be the smallest 4-digit positive integer greater than or equal to 2016 with the following property: there exists a positive integer $S$ such that
$$
S=\sqrt{a+\sqrt{b+\sqrt{c+\sqrt{d+S}}}}
$$
where $a, b, c, d$ are, in order, the thousands, hundreds, tens and units digits of $n$. What is the value of $n$?
$$
S=\sqrt{a+\sqrt{b+\sqrt{c+\sqrt{d+S}}}}
$$
where $a, b, c, d$ are, in order, the thousands, hundreds, tens and units digits of $n$. What is the value of $n$?