A5. A group of chess players and a group of checkers players spend a weekend at a sports center. Each chess player plays one match against every other chess player, and each checkers player plays one match against every other checkers player. Chess players and checkers players do not play matches against each other. In total, 100 matches are played.

Determine the sum of the number of chess players and the number of checkers players.
A5. If the group of checkers players consists of 6 people, then each player plays against 5 other players, for a total of $6 \times 5$ games, but each game is counted twice, so there are 15 games played.

In general: with $n$ checkers players, $\frac{n(n-1)}{2}$ games are played. We make a list:

| antd | players | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | $\geq 15$ |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| antd | games | 1 | 3 | 6 | 10 | 15 | 21 | 28 | 36 | 45 | 55 | 66 | 78 | 91 | $\geq 105$ |

Only the numbers 45 and 55 add up to 100. Therefore, there are a total of $10+11=21$ players.