The probability that Sue completes all n puzzles correctly is given by \((0.75)^n\).

We need to find the smallest n such that \((0.75)^n < 0.06\).

Taking logarithms on both sides, we have:

\(\log((0.75)^n) < \log(0.06)\)

\(n \cdot \log(0.75) < \log(0.06)\)

\(n > \frac{\log(0.06)}{\log(0.75)}\)

Calculating the right-hand side gives \(n > 9.78\).

Since n must be an integer, the smallest possible value is \(n = 10\).