Logic Riddles

Question: There are 1600 people sitting around a circular table. The first person (person 1) has a sword and kills the second person then hands it to the next alive person (in this case person 3). Person 3 stabs person 4 and gives the sword to person 5. This goes on until person 1499 kills person 1500. Then person 1 kills person 3 and so on. This is repeated until there is only a single person remaining.

Who remains in the end?

Question: You are in a room with two metal rods and no other metal. One of them is magnetized and the other is not.

How can you determine which one is magnetized and which is not?

Question: There is an island with exactly 201 residents, 100 with blue eyes, 100 with brown eyes, and the island leader (who has green eyes). To leave the island, one must know their own eye color. There are no reflective surfaces on the island and no on can communicate with each other other than the leader to the residents. No one on the island knows how many of each eye color there is. Everyone on the island is a perfect logician, meaning that if there us a solution they'll find it. Every morning the leader gives anyone a chance to leave the island by guessing their eye color. One morning, the leader gathers all 200 residents to make an announcement, he says "at least 1 person on this island has blue eyes" How many people leave the island and in how many days after the announcement? Notes: this is known as one of the hardest riddles ever

Question: In the harbor of a small town, there is a large boat. Coming off of the boat is a ladder reaching down so that the bottom rung is just above the surface of the water. As the tide comes in, the water rises at 1 foot every 30 minutes, and continues like this for 3 hours. If the rungs are each 1 foot apart, how many rungs are under water when the tide stops rising?