Math Riddles

Question: You are playing a game of dodge ball with two other people, John and Tom. You're standing in a triangle and you all take turns throwing at one of the others of your choosing until there is only one person remaining. You have a 30 percent chance of hitting someone you aim at, John has a 50 percent chance, and Tom a 100 percent change (he never misses). If you hit somebody they are out and no longer get a turn.

If the order of throwing is you, John, then Tom; what should you do to have the best chance of winning?

Question: An ant gets onto one end of a tight rope that is 1 meter long. The ant is traveling at 1 centimeter per second, but the entire rope is being stretched an extra 1 meter (1,000 centimeters) a second (it can be stretched forever).

Will the ant ever reach the other end of the rope?

Question: There are 100 passengers boarding a 100 passenger airplane. When passenger 1 gets onto the plane, he is dissoriented, so he randomly picks a seat. Each of the remaining passengers (2, 3, 4, etc.) get onto the plane and take their seat if it is available or picks one of the remaining seats at random if it is not.

What is the chance that the last passenger (passenger 100) will get his seat?

Question: There are 100 prisoners lining up to go to jail. Each prisoner is wearing a hat that is either black or white. The prisoners don't know their own hat color, just the hat color of those in front of them in line (the first prisoner in line can't see anyone's hat and the last prisoner can see everyone's hat except their own). Starting from the back, one of the guards asks each prisoner what color their hat is. If they are correct they get to go free but if they are wrong they go to jail.If the prisoners get to discuss a plan, how can at least 99 of them be saved?

Question: Four people need to cross a bridge in 17 minutes in the middle of the night. The bridge can only hold two or less people at any time and they only have one flashlight so they must travel together (or alone). The flashlight can only travel with a person so every time it crosses the bridge it must be carried back. Tom can cross in 1 minute, John can cross in 2 minutes, Sally can cross in 5 minutes, and Connor can cross in 10 minutes. If two people cross together they go as fast as the slower person.How can they cross the bridge in 17 minutes or less?