1. During the night shift, four attendants ate a whole barrel of pickles. If assistant Murr had eaten half as much, a tenth of the barrel would have remained. If lab assistant Trotter had eaten half as much, an eighth of the barrel would have remained. If intern Glupp had eaten half as much, a quarter of the barrel would have remained. What part of the barrel's contents would remain if orderly Stoss had eaten half as much?
# Solution

Suppose each ate half as much. Then exactly half of the barrel would have been eaten. From the remaining half, Murr, Trotta, and Glupp would have eaten $\frac{1}{10}$, $\frac{1}{8}$, and $\frac{1}{4}$ of the barrel, respectively. Therefore, the portion for Schtos would be

$$
\frac{1}{2}-\frac{1}{10}-\frac{1}{8}-\frac{1}{4}=\frac{1}{40}
$$

Answer: $\frac{1}{40}$ of the barrel.