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

Cheers!

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