## Task B-1.2.

Ivo, Alen, Vanja, Marko, and Saša are chefs in a hotel. Alen and Marko are responsible for preparing breakfast and lunch, Ivo and Vanja work on preparing lunch and dinner, while Saša is available for all three meals. In how many ways can their daily cooking schedule be arranged if each meal is prepared by exactly two chefs, and a chef who works must be assigned to exactly two meals? Can each chef have at least one day off in the week with such a daily schedule? Explain.
## Solution.

Lunch can be cooked by all chefs, so we will first choose the person who will cook lunch. There are several cases:

1. If lunch is cooked by Alen or Marko, they must also cook breakfast, so for dinner, we would need to engage two new chefs who would work on only one meal. Therefore, Alen and Marko cannot cook lunch together. The same situation applies to Ivo and Vanja.
2. If lunch is cooked by Saša and Alen, then Alen must cook breakfast. However, if Marko were to cook breakfast with Alen, Marko would also have to cook lunch, but lunch is already being cooked by two chefs. The same situation would occur in any other combination where Saša cooks lunch, so Saša cannot cook lunch.
3. If lunch is cooked by Alen and Ivo, then breakfast is cooked by Alen and Saša, and in this case, Saša must cook dinner, and with him, Ivo must cook dinner. If Saša were not to cook breakfast, then in this case, Marko would have to cook breakfast, but then he would also have to cook lunch, which is already occupied. Therefore, Saša must cook breakfast and dinner every day.
4. Each schedule is defined by the pair that cooks lunch, and there are four such pairs, so there are 4 schedules in total. Since Saša must work every day, he will not be able to have a free day.