Problem 9.4. In city $\mathrm{N}$, there are exactly three monuments. One day, a group of 42 tourists arrived in this city. Each of them took no more than one photo of each of the three monuments. It turned out that any two tourists together had photos of all three monuments. What is the minimum number of photos that all tourists could have taken in total?
Answer: 123.

Solution. Let's number the three monuments. Note that the photo of the first monument is missing from no more than one tourist (otherwise, we could choose two tourists who, in total, have photos of no more than two monuments), so at least $42-1=41$ photos of the first monument were taken. Similarly, at least 41 photos of the second and third monuments were taken. Therefore, a total of at least $41 \cdot 3=123$ photos were taken.

Exactly 123 photos could have been taken, for example, if 1 tourist did not take any photos, and the other 41 each took one photo of each monument. It is clear that in this case, all conditions of the problem are satisfied.