Math Riddles

Question: A grandfather has a broken grandfather clock that is off by a minute every hour (too fast). He figures out a way, while keeping it running at the same rate, to make the clock say the correct time twice a day.

How could he do this?

Question: What is the difference between a dollar and a half and thirty five-cents?

Question: Thomas has missed an excessive number of days of school, so he must meet with Principal Davis. Mr. Davis asks him "Why on Earth have you missed so many days?"

Thomas replies "There just isn't enough time for school. I need 8 hours of sleep a day, which adds up to about 122 days a year. Weekends off is 104 days a year. Summer vacation is about 60 days. If I spend about an hour on each meal, that's 3 hours a day or 45 days a year. I need at least 2 hours of exercise and relaxation time each day to stay physically and mentally fit, adding another 30 days.

Add all of that up and you get about 361 days. That only leaves 4 days for school."

The principal knows Thomas is full of it, but can't figure out why. Where is Thomas going wrong?

Question: How many people do you need to have the odds be in favor (at least 50% chance) of two people having the same birthday?

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?