Percentiles and Box Plots · Superchallenge problem

Quartiles are the medians of the lower and upper halves of the data (the median excluded when $n$ is odd), and a value is an outlier if it is more than $1.5 \cdot \text{IQR}$ below $Q_1$ or above $Q_3$. What is the smallest number of values $n$ that a data set can have and still contain an outlier?