The glasses sound in total 15 times. This results from the following considerations:
- The first party guest clinks with the five other guests, thus the glasses sound 5 times.
- The second guest clinks with all others except the first one. The glasses sound 4 times.
- The third guest clinks with all others except the first and second guest. The glasses sound 3 times.
- The fourth guest clinks only with the fifth and sixt guests, thus the glasses sound 2 times.
- Finally, guests five and six clink on each other while the glasses sound only 1 time.
Expressed in a formula, that means:
The sound of glasses = 0,5 * n * (n - 1)
n = Number of guests
The sound of glasses = 0,5 * 6 (6-1) = 15