Serviceline Industrial Sensors
Serviceline Explosion Protection

# Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 1, February 2015

## Cheers!

How often do the glasses ring?

Three couples come together for a New Year's party. Shortly before midnight, they are counting the last seconds until it`s finally 12:00 a.m.. With a glass of champagne each, they toast the New Year.
How often do the glasses ring if everyone clinks glasses with each other in turn?

## Solution

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