Darts needed for a 90 percent bullseye chance

Each dart Yugi throws hits the bullseye with probability $0.1$, independently of all other throws. What is the fewest number of throws that gives him at least a $90\%$ chance of at least one bullseye?

$22$. All $n$ throws miss with probability $0.9^n$, so we need $0.9^n\le0.1$, i.e. $n\ge\tfrac{\ln 0.1}{\ln 0.9}\approx21.85$.