Problem 6. An excursion group of 6 tourists is visiting attractions. At each attraction, three people take photos, while the others photograph them. After what minimum number of attractions will each tourist have photos of all other participants in the excursion?

Answer: after 4 attractions.
Solution. Evaluation. A total of $6 \cdot 5=30$ photographs need to be taken (considering only photographs between two people $A$ and $B$, that is, if person $A$ photographs 3 other participants $B, C, D$ in one photograph - this counts as 3 photographings $A \rightarrow B, A \rightarrow C, A \rightarrow D$).

At one landmark, no more than $3 \cdot 3=9$ new photographings can occur. Thus, three landmarks are insufficient.

We can provide an example of how to organize the photographings around four landmarks. Let's number the people from 1 to 6. Then we can organize everything as follows:

- $(123) \rightarrow(456)$
- $(145) \rightarrow(236)$
- $(256) \rightarrow(134)$
- $(346) \rightarrow(125)$.

It is not difficult to verify that each person will photograph every other person at least once.

## Criteria

4 6. A complete and justified solution is provided.

In the absence of a correct solution, the highest applicable criterion from those listed below is used:

2 6. It is proven that the tourists need to visit at least 4 landmarks, but the method of photographing is not specified

2 6. A method of photographing at four landmarks is specified to meet the conditions of the problem, but the evaluation is not proven

0 6. The correct answer is provided, but there is no justification

0 6. The problem is not solved or is solved incorrectly.