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On day one, there are $100$ particles in a laboratory experiment. On day $n$, where $n \geq 2$, one out of every $n$ particles produces another particle. If the total number of particles in the laboratory experiment increases to $1000$ on day $\mathrm{m}$, then $\mathrm{m}$ equals

1. $19$
2. $17$
3. $16$
4. $18$

1