examday

/TMUA

For each $n=1,2,\ldots,100$, the statement $S_n$ is:

At least $n$ of the integers $m$ with $1\leq m\leq100$ have $m^2-1$ divisible by $24$.

Exactly how many of the statements $S_1,S_2,\ldots,S_{100}$ are true?