There are 8 people on the winning Trivia team, and each person shakes hands with each other person once. How many handshakes take place?

This classic puzzle can be solved by thinking systematically. Imagine the eight people lining up. The first person shakes hands with the other seven people. The second person has already shaken hands with the first, so they only need to shake hands with the remaining six. The third person then shakes hands with the five people who they haven't greeted yet. This pattern continues, with each person shaking one fewer hand than the person before them, until the second-to-last person shakes only the last person's hand. This results in the simple sum of 7 + 6 + 5 + 4 + 3 + 2 + 1.

This type of puzzle is a well-known introduction to the mathematical field of combinatorics, which is concerned with counting and arranging objects. For any number of people 'n', the number of handshakes can be found with the formula n(n-1)/2. In this case, with 8 people, it would be 8 multiplied by 7, which equals 56. The reason you divide by two is that every handshake involves two people, and this formula initially counts each handshake twice (once for each person involved). Therefore, dividing by two gives the correct unique number of handshakes.

While it seems like a simple brain-teaser, this problem has real-world applications and historical roots. For instance, the nine justices of the U.S. Supreme Court have a tradition of shaking hands with every other justice before they begin a session. The principles of combinatorics used to solve this puzzle date back to ancient India and China and were more formally developed in the 17th century by famous mathematicians like Blaise Pascal and Pierre de Fermat. It's a foundational concept in probability theory and computer science.