Aleš, Bára, Cyril, Dana, Eva, František, and Gábina became champions in table football at their schools and met for a two-day tournament to determine the overall winner. Each of these seven children was to play one game with each of the others during the tournament. On the first day of the tournament, Aleš played one game, Bára two games, Cyril three, Dana four, Eva five, and František six.

How many games did Gábina play on the first day?

(L. Hozová)
There were seven children, so each could play at most six games. František played six games, so he played with every child present.

Aleš played one game, so he played with no one other than František. Eva played five games, so she played with everyone except Aleš.

Bára played two games, so she played with no one other than František and Eva. Dana played four games, so she played with everyone except Aleš and Bára.

Cyril played three games, and that was with František, Eva, and Dana.

Gábina played with František, Eva, and Dana, so Gábina played three games.

Note. The previous conclusions are clearly visible in the table:

|  | $\mathrm{A}$ | $\mathrm{B}$ | $\mathrm{C}$ | $\mathrm{D}$ | $\mathrm{E}$ | $\mathrm{F}$ | $\mathrm{G}$ |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| $\mathrm{A}$ | - |  |  |  |  | $*$ |  |
| $\mathrm{B}$ |  | - |  |  | $*$ | $*$ |  |
| $\mathrm{C}$ |  |  | - | $*$ | $*$ | $*$ |  |
| $\mathrm{D}$ |  |  | $*$ | - | $*$ | $*$ | $*$ |
| $\mathrm{E}$ |  | $*$ | $*$ | $*$ | - | $*$ | $*$ |
| $\mathrm{F}$ | $*$ | $*$ | $*$ | $*$ | $*$ | - | $*$ |
| $\mathrm{G}$ |  |  |  | $*$ | $*$ | $*$ | - |