Los Angeles Math Circle

9/25 -- Junior Circle: Hotel Infinity I (Alyssa Perez)

Far away, in a distant galaxy, there is hotel called Hotel Infinity. True to its name, the hotel has infinitely many rooms. Currently, all the rooms are taken. Then, a guest arrives. Can you find a space for the new guest? What if 10 guests arrive? Can you combine two such hotels into one? In this first meeting related to our studies of infinity, we will solve a series of problems related to Hotel Infinity.