24. From the results table of a single-round football tournament with 10 teams, only the total number of goals scored and conceded for each team remained. This was enough for the mathematician to restore the score in each match. What is the smallest number of these 20 numbers that could have been zeros?
Answer: 0. Solution. If the total number of goals scored by team $A$ equals the total number of goals conceded by the other teams, and the same is true for the goals conceded by team $A$ and the total number of goals scored by the other teams, then all goals were scored and conceded only in matches involving team $A$. Therefore, the score against all teams except $A$ is the score in the match against team $A$, and all other matches ended in $0: 0$.