First discover the wording of the query: “Patrick requested everybody how many individuals they performed towards, and located that every one answered with a distinct quantity”
Which means
Patrick himself might have performed the identical variety of video games as one of many different gamers.
Specifically, as famous within the feedback
No one might 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 companion and so their companion have to be the one who performs 0 matches (since each different participant performs not less than one match). Equally, the one who performed 13 matches performs everybody besides the one who performed 0 and their companion 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.
Lastly, the one who performed 7 matches have to be coupled with the remaining individual, Patrick, who should even have performed 7.
Therefore, we deduce that Rachel performed
7 matches