## Task 1 - 020731

In a prize competition, it was necessary to correctly match the pictures of 4 different buildings to 4 named cities. 12 percent of the entries had everything correct, twice as many had two buildings correct, and four times as many had one building correct. 240 submitted solutions were completely wrong.

a) How many solutions were submitted?

b) How many entrants had 0, 1, 2, 3, and 4 pairs correctly matched?
First, it is noted that it is not possible to correctly assign three buildings and one incorrectly. $12 \%+24 \%+48 \%=84 \%$ had at least one building correct. Therefore, the remaining $16 \%$ correspond to the 240 completely incorrect submissions. This means that a total of 1500 solutions were submitted, of which 240, 720, 360, 0, and 180 had exactly 0, 1, 2, 3, and 4 pairs correct, respectively.