The king gave the mason Václav the task of building a wall 25 cm thick, 50 m long, and 2 m high. If Václav worked without breaks and at a constant pace, he would build the wall in 26 hours. However, according to the valid royal regulations, Václav must adhere to the following conditions:

- During the work, he must take exactly six half-hour breaks.
- At the beginning of the work and after each half-hour break, when he is sufficiently rested, he can work one quarter faster than the normal pace, but no longer than one hour.
- Between breaks, he must work at least 3/4 of an hour.

What is the shortest time in which Václav can complete the assigned task?

(J. Norek)

Hint. Can Václav schedule his breaks so that he fully utilizes his rested state?
Václav has to take exactly six half-hour breaks. This will cost him $6 \cdot 1 / 2=3$ hours. He can schedule the breaks so that at the start of work and after each break, he can work for a full hour at an increased pace (for example, with an even distribution). This will gain him $7 \cdot 1 / 4$ hours, i.e., 1 hour and 45 minutes.

Without breaks, at a normal pace, Václav would work 26 hours. With all the mandatory breaks and all the allowed increases in pace, Václav would work $26+3-7 / 4$ hours, i.e., 27 hours and 15 minutes. This is the shortest time in which he can complete his task.