Light Emitting Hindenburg

Lothar is organizing a concert tour for a rock band of his friends. The tour will take place in November, and there will be at most one concert per day. The tour is expected to be large-scale, and many musicians will want to participate. The number of musicians in the tour is strictly fixed and cannot be changed. All musicians participating in the tour must be present at each concert.

The good news for Lothar is that the number of candidate musicians is at least equal to the required number of participants for the tour. The bad news is that an individual musician may be unavailable throughout the month, and the schedules of different musicians vary significantly.

Some time ago, Lothar wrote the core of a computer scheduling system and now uses it to organize the tour. He repeatedly and randomly selects a group of musicians of a given size and allows the system to compute a feasible tour schedule. The system relies on a very specific data format: musicians’ schedules and tour schedules are represented as numerical codes. The days of November are denoted by their numbers: 1, 2, \dots, 30.

For each musician, each day in November has a specific numerical code. A day labeled $l$ is encoded as 2^{30-l} if the musician is available on that day, and $0$ otherwise. The code of a musician's schedule is the sum of all codes of their available days.

For a group of musicians, each November day is also assigned a numerical code. A day labeled $l$ is encoded as 2^{30-l} if all musicians in the group are free on that day, and $0$ otherwise. The code of the group’s availability is the sum of the codes of all days for the group.

For some reason, Lothar considers the optimal tour to be the one in which the code of the musicians' group availability is maximized.