do not cheat and use google. Answer 3 numbers below :) THE PIRATE GAME 1. Suppose there are 100 gold coins and 5 pirates. The 5 pirates put 5 numbers (1,2,3,4,5) in a hat and randomly pick out a number. This process determines the sequence in which the pirates proceed in the game. The pirate who picked #1 gets to decide how many coins to allocate to himself and to every other pirate. Then all the pirates vote on this allocation. If AT LEAST HALF of the pirates (including the allocator) consider this a suitable allocation, then the game ends. However, if the allocation is not approved by at least half of the pirates, the pirate #1 is killed and the game starts over with the initial order (i.e. with 4 pirates and #2 as the allocator, #3 as the next guy, #4 as two from the beginning, etc). This process (i.e. vote and either end the game or kill the allocator) continues until the game ends or only 2 pirates are left. Assuming that all pirates are strictly rational, how will the coins be allocated? How many Pirates are killed? The Hat Game 2. Three people are sitting in a circle. Black hats have been placed on their head. They have been told that their hat could be white or black. They are then told that at least one hat is black. The players cannot see their own hat color, but they can see the colors of the other players' hats. There are multiple rounds and each round a player may either state a guess as to the color of their own hat or remain silent. If all of them guesses their own hat color correctly, and no one guesses incorrectly, they will share a prize. If there are no correct guesses, or if there are any incorrect guesses, they lose. What is the minimum amount of rounds it takes for each person to know what color their hat is and why? The line hat game 3. There are 100 prisoners that will be lined up each with black or white hat on their head tomorrow. Starting from the back of the line a guard will ask each player what color his/her hat is and if they guess incorrectly the guard will execute the prisoner. They will be in a single file line, and they can only look ahead. They can only guess the color of their hat. The prisoners cannot communicate during the line up but can come up with a strategy the day before the line up. What is the best strategy that minimizes the number of prisoners that are executed? How many are executed