First discover the wording of the query: “Patrick requested everybody how many individuals they performed in opposition to, and located that every one answered with a special quantity”

This signifies that

Patrick himself might have performed the identical variety of video games as one of many different gamers.

In specific, as famous within the feedback

Nobody may have performed 15 matches, therefore Patrick heard every reply between 0 and 14 precisely as soon as.

Now observe that

The one who performed 14 matches performs everybody besides their accomplice and so their accomplice have to be the one who performs 0 matches (since each different participant performs at the very least one match). Similarly, the one who performed 13 matches performs everybody besides the one who performed 0 and their accomplice so have to be coupled with the one who performed 1 match.

Following this line of reasoning additional, the one who performed 12 matches is coupled with the one who performed 2, the one who performed 11 is coupled with the one who performed 3… and the one who performed 8 have to be coupled with the one who performed 6.
Finally, the one who performed 7 matches have to be coupled with the remaining particular person, Patrick, who should even have performed 7.

Hence, we deduce that Rachel performed

7 matches