4. When entering the shooting range, the player pays 100 rubles to the cashier. After each successful shot, the amount of money increases by $10 \%$, and after each miss - decreases by $10 \%$. Could it be that after several shots, he ends up with 80 rubles and 19 kopecks?
# Solution:

An increase of $10 \%$ means multiplying by 1.1. A decrease of $10 \%$ means multiplying by 0.9.

80 rubles 19 kopecks $=8019$ kopecks.

Let's factorize 8019: $8019=3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 11=9 \cdot 9 \cdot 9 \cdot 11$.

Therefore, after three misses and one hit, the player will have:

$100 \cdot 0.9 \cdot 0.9 \cdot 0.9 \cdot 1.1=80.19$, i.e., 80 rubles 19 kopecks.

Answer: yes, it could.