Liesl has a bucket. Henri drills a hole in the bottom of the bucket. Before the hole was drilled, Tap A could fill the bucket in 16 minutes, tap B could fill the bucket in 12 minutes, and tap C could fill the bucket in 8 minutes. A full bucket will completely drain out through the hole in 6 minutes. Liesl starts with the empty bucket with the hole in the bottom and turns on all three taps at the same time. How many minutes will it take until the instant when the bucket is completely full?
Since taps A, B and C can fill the bucket in 16 minutes, 12 minutes and 8 minutes, respectively, then in 1 minute taps A, B and C fill $\frac{1}{16}, \frac{1}{12}$ and $\frac{1}{8}$ of the bucket, respectively.

Similarly, in 1 minute, $\frac{1}{6}$ of the bucket drains out through the hole.

Therefore, in 1 minute with the three taps on and the hole open, the fraction of the bucket that fills is $\frac{1}{16}+\frac{1}{12}+\frac{1}{8}-\frac{1}{6}=\frac{3+4+6-8}{48}=\frac{5}{48}$.

Thus, to fill the bucket under these conditions will take $\frac{48}{5}$ minutes.

ANSWER: $\frac{48}{5}$ minutes