SMMG Riddles

Here you'll find some fun riddles and fun math exercises related to things we've talked about at SMMG sessions. These riddles are all incredibly hard, and will almost certainly require a lot of time to solve them! Keep trying, and please feel free to reach out with questions on these riddles!

  1. You come across two doors and know that one of them has gold behind it and the other has a PERSON EATING TIGER behind it. Each door is guarded by a guard. You know one of them tells the truth and one of them always lies, but you don't know who is guarding what door! You get to ask one guard one question. What one question can you ask to find the gold door?
  2. Can you cut this shape into four pieces of the same shape and area using only lines and line segments? (Thanks to Lorenzo Sadun for this riddle!)
  3. You are at the store buying a talking robot. The storekeeper tells you that there are three robots: one that always tell the truth, one that always lies, and one that answers randomly! You don't know which is which, and you want to get either the one that always tells the truth or the one that always lies (so you know what you're getting). You get to ask one robot one question. What question should you ask a robot to make sure you get the truth telling robot or the lying robot?
  4. Casandra, Yixian, and Tom are playing a ping pong tournament where two people start playing a game, and then the loser swaps out with the person sitting out. Casandra played 17 games, Yixian played 15 games, and Tom played 10 games. Who lost the second game, and why?
  5. Pick a positive integer m. Show that if m isn't even and m isn't divisible by 5, then either 9 is divisible by m, or 99 is divisible by m, or 999 is divisible by m, or 9999 is divisible by m, or 99999 is divisible by m, or... (Thanks to Lorenzo Sadun for this riddle!)
  6. If you think you have a solution to one of these, feel free to email us with your solution and we will check it for you! Don't forget to not only include an answer, but why you think your answer is correct!