9. At a party, every 3 rd guest receives a key chain and every 8 th guest recelves a mug. What is the position of the second guest who will receive both a key chain and a mug?

The key chain is given to every 3rd guest, while the mug is given to every 8th guest. To find the position of guests who receive both items, we need to identify the least common multiple (LCM) of 3 and 8, which is 24. This means every 24th guest will receive both a key chain and a mug. The first guest to receive both is at position 24, and the second guest will be at position 48. So, the position of the second guest who will receive both a key chain and a mug is 48. Fun fact: The concept of finding least common multiples is not only useful for parties but is also a cornerstone in scheduling events where multiple cycles overlap. Think of it like coordinating who gets to use the last piece of cake based on their turn - the LCM helps efficiently plan it out! If you enjoy these numerical puzzles, consider exploring modular arithmetic! It’s a fascinating area that deals with remainders and can deepen your understanding of these kinds of problems. There are also plenty of online games and apps that can help you practice and improve your skills in a fun, engaging way!