Logic Riddles

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?

Question: There are four men: Abe, Butch, Cam, and Dan. There are four hats: two white and two black. They each get a hat: Abe gets black, Butch gets white, Cam gets black, and Dan gets white. They don't know what hat color they have. Abe goes into a room so that no one can see his hat. The others line up in front of the door in the order Butch, Cam, and Dan (Butch can't see the others hats, Cam can see Butch's, and Dan can see Cam and Butch's hats). Whoever can figure out their hat color first wins $1,000. If they are wrong they are out of the running.

Which man can figure out his hat color without a doubt?