# Task No. 4.1

## Condition:

Six friends live in a small town in southern France. One day they decided to go to Paris together for one day and see the attractions - the Eiffel Tower, the Louvre, Notre-Dame Cathedral, the Rodin Museum, the Bois de Boulogne, and the Champs-Élysées. The friends agreed to split up and see them separately, and since time was limited, each chose three attractions and visited only those. In the evening, they met and began discussing which places each of them had visited. Each named their three attractions, but two of the friends accidentally got everything mixed up and instead of the places they visited, they named the three places they did not visit. Here is the list of places each friend named:

- Friend 1: Eiffel Tower, Louvre, Notre-Dame Cathedral
- Friend 2: Eiffel Tower, Louvre, Rodin Museum
- Friend 3: Notre-Dame Cathedral, Rodin Museum, Bois de Boulogne
- Friend 4: Notre-Dame Cathedral, Rodin Museum, Champs-Élysées
- Friend 5: Notre-Dame Cathedral, Louvre, Rodin Museum
- Friend 6: Eiffel Tower, Notre-Dame Cathedral, Rodin Museum

When the friends later started sorting through the photos, tickets to the museums, and discussing what they liked, it turned out that each place was visited by exactly three of them. Help to restore who of the friends got everything mixed up and named the places they did NOT visit. In each field, write separately the numbers of the friends who meet the condition.
# Answer:

$\circ 5$

० 6

## Exact match of the answer -1 point

## Solution.

Five people said they visited Notre-Dame Cathedral, but in reality, only three did. This means that at least two of them were mistaken, and therefore the one who did not mention the Cathedral (friend 2) must have been correct. Similarly, the first friend must have been correct as well, since he alone did not mention the Rodin Museum. Now, notice that the Bois de Boulogne was mentioned only by friend 3. This means that among the remaining, two must have been mistaken, since only three could have not visited the cathedral, and thus the third friend must have been correct. By the same logic, friend 4 must have been correct as well, since he alone mentioned the Champs-Élysées. The only ones left are friends 5 and 6, who must have been mistaken. Let's reconstruct the correctly visited places and verify that everything fits:

Actually visited attractions:

Friend 1: Eiffel Tower, Louvre, Notre-Dame Cathedral

Friend 2: Eiffel Tower, Louvre, Rodin Museum

Friend 3: Notre-Dame Cathedral, Rodin Museum, Bois de Boulogne

Friend 4: Notre-Dame Cathedral, Rodin Museum, Champs-Élysées

Friend 5: Eiffel Tower, Bois de Boulogne, Champs-Élysées

Friend 6: Louvre, Bois de Boulogne, Champs-Élysées

Everything fits: each attraction was visited by exactly three friends.

Thus, the answer is that friends 5 and 6 were mistaken.