ANSWER: Let's denote the total number of persons who participated in the tournament as \( P \). If no couple played in a match, it means that each match involved two different persons. Therefore, the number of matches played is half the total number of persons (\( P/2 \)).
The problem states that the number of matches played is 840. So we can set up the equation:
\[ \frac{P}{2} = 840 \]
To find \( P \), we can multiply both sides of the equation by 2:
\[ P = 2 \times 840 \]
\[ P = 1680 \]
So, the total number of persons who participated in the tournament is 1680.
