Four couples and one single person attend a party. At the time they enter, none of the guests know anyone else besides their partners, if they came with one. Once in the room, everyone wanders around individually and mingles, and if they meet someone new they introduce themselves. After a few hours, a buzzer goes off and everyone stops talking. Every person has made a unique number of introductions ranging from zero to eight. With this info, how many introductions has the single person made?
Facts for clarity:
- 9 people total, 4 couples and one stag
- Each person has a unique introduction count, ranging from 0 - 8
- Couples do not introduce themselves to their partners
You have posed this question incorrectly.
Given four couples (AB, CD, EF, GH) and an individual (I), no coupled person can introduce themselves to more than seven other people at the party (for instance, A can introduce themselves to CDEFGHI). This leads us to conclude that I must have introduced themselves to eight people. However, this results in a contradiction — if I introduced themselves to all eight other people, it is impossible for any of the remaining partygoers to have met nobody.