Logic Riddles

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: 500 is at my end and my start, yet 5 is at my heart.
The first letter and the first number make me complete.
My name is that of a king.

What am I?

Question: Jack is taking a tour through a museum's American Presidents exhibit. The person leading the tour tells him "We have a picture of each presidency. Currently Barack Obama is the 43rd person to hold the office." But Jack quickly realizes that there are 44 pictures on the wall. But while walking through the exhibit he realizes why this is.

Why is there one too many photos?

Question: Five pirates are parting ways after finding a treasure of 100 pieces of gold. The pirates decide to split it based on a vote. Each pirate, from oldest to youngest, gets to propose a plan on how to split the gold.

If at least 50 percent of the other remaining pirates agree on the plan, that is how they will split the gold. If less than 50 percent of the pirates agree, the pirate who came up with the plan will be thrown overboard. Each pirate is smart, greedy, and wants to throw as many others overboard as possible without reducing the amount of gold they get.

What plan can the first (oldest) pirate propose to live and get as much gold as possible?

Question: A bank is getting robbed and one of the robbers tells one of the tellers to give him all of the money. The teller tells him she doesn't have access to it.

Suddenly the phone rings. The robber tells the teller to answer it and not give them away. She picks up the phone and it happens to be her mother. She tells her mother "Is this an emergency mom? Call me when I get home, I could use some help painting." Then she hangs up.

The robbers continue to try to get into the vault but twenty minutes later the police show up with the tellers mom and arrest them all.

How did the police know about the robbery?