A number theory problem by Lee Wall

Number Theory Level 3

Let \(S\) be the set of integers that leave a remainder of \(1\) when divided by \(2\), a remainder of \(2\) when divided by \(3\), and a remainder of \(3\) when divided by \(4\). How many integers in the interval \([0, 10^{4}]\) belong to \(S\)?