Percentiles and Box Plots · Superchallenge problem

The data set $1, 2, 3, \ldots, 20$ is extended by adding $k$ copies of the value $100$. Quartiles are the medians of the lower and upper halves (the median excluded when the count is odd), and outliers use the $1.5 \cdot \text{IQR}$ rule. What is the smallest $k$ for which $100$ is NOT an outlier?