The natural number $n$ was multiplied by $3$, resulting in the number $999^{1000}$. Find the unity digit of $n$.
1. We start with the given equation: 
   \[
   3n = 999^{1000}
   \]
2. To find the unity digit of \( n \), we first determine the unity digit of \( 999^{1000} \). Notice that:
   \[
   999 \equiv -1 \pmod{10}
   \]
3. Therefore:
   \[
   999^{1000} \equiv (-1)^{1000} \pmod{10}
   \]
4. Since \( (-1)^{1000} = 1 \):
   \[
   999^{1000} \equiv 1 \pmod{10}
   \]
5. This tells us that the unity digit of \( 999^{1000} \) is 1.
6. Now, we need to find the unity digit of \( n \) such that:
   \[
   3n \equiv 1 \pmod{10}
   \]
7. We test the possible unity digits for \( n \) to satisfy this congruence:
   - If \( n \equiv 0 \pmod{10} \), then \( 3 \cdot 0 \equiv 0 \pmod{10} \)
   - If \( n \equiv 1 \pmod{10} \), then \( 3 \cdot 1 \equiv 3 \pmod{10} \)
   - If \( n \equiv 2 \pmod{10} \), then \( 3 \cdot 2 \equiv 6 \pmod{10} \)
   - If \( n \equiv 3 \pmod{10} \), then \( 3 \cdot 3 \equiv 9 \pmod{10} \)
   - If \( n \equiv 4 \pmod{10} \), then \( 3 \cdot 4 \equiv 2 \pmod{10} \)
   - If \( n \equiv 5 \pmod{10} \), then \( 3 \cdot 5 \equiv 5 \pmod{10} \)
   - If \( n \equiv 6 \pmod{10} \), then \( 3 \cdot 6 \equiv 8 \pmod{10} \)
   - If \( n \equiv 7 \pmod{10} \), then \( 3 \cdot 7 \equiv 1 \pmod{10} \)
   - If \( n \equiv 8 \pmod{10} \), then \( 3 \cdot 8 \equiv 4 \pmod{10} \)
   - If \( n \equiv 9 \pmod{10} \), then \( 3 \cdot 9 \equiv 7 \pmod{10} \)
8. From the above, we see that \( n \equiv 7 \pmod{10} \) is the only solution that satisfies:
   \[
   3n \equiv 1 \pmod{10}
   \]

The final answer is \( \boxed{7} \).