81. At exactly 24:00, the battery received an order to begin artillery preparation at the earliest time that will pass until the hour and minute hands overlap again. At what time should the artillery preparation begin?
81. In 1 hour, the minute hand makes a full revolution and will point to 12, while the hour hand will have traveled $\frac{1}{12}$ of the circumference and will point to 1. This means that after 1 hour, the minute hand, following the hour hand, will be at a distance equal to $\frac{1}{12}$ of the circumference from it. Since in 1 hour the minute hand will travel $\frac{11}{12}$ of the circumference more than the hour hand ($1-\frac{1}{12}=\frac{11}{12}$), it will "catch up" with the hour hand after 1 hour plus an additional $\frac{1}{11}$ hour $\left(\frac{1}{12} : \frac{11}{12} = \frac{1}{11}\right)$. Therefore, the hour and minute hands will coincide again, starting from 12, after $1 \frac{1}{11}$ hours, i.e., at 1 hour 5 minutes 27 seconds. This is the time (to the nearest second) when the artillery preparation should begin.