4. Seven coworkers (Maria, Iskra, Lile, Petre, Mile, Todor, and Kosta) have lunch together in three restaurants ($P, Q$, and $R$).

Maria goes to a restaurant only on Wednesday.

Iskra and Mile can never be in the same restaurant at the same time.

Lile does not go to a restaurant if Maria does not go.

Petre and Kosta will not go to the same restaurant together unless Iskra goes.

Mile does not go to restaurant $Q$.

If six of the coworkers have lunch together on Wednesday in one of the restaurants, which coworker will be absent?

What is the maximum number of coworkers that can have lunch together on Tuesday?
Solution. It is clear that either Mile or Iskra will be absent. If Iskra is absent, then Petre and Kosta will not be in the restaurant together, so in that case, at most 5 colleagues will have lunch together. According to this, if six colleagues have lunch together on Wednesday, Mile will be absent.

On Tuesday, Maria does not go to lunch, which means Lile will not go to lunch either. Since Iskra and Mile never have lunch together, it follows that on Tuesday, at most four colleagues can have lunch together.

## 2nd year