Question: A man in prison has a visitor. Afterward a guard asks the inmate who the visitor was to him. The inmate replies: "brothers and sisters I have none, but that man's father is my father's son." Who was the visitor to the inmate?
Answer: His son.
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?
Answer: Person 1153.
If you have any number of people equal to a power of 2 (2, 4, 8, etc.) then the first person will be the last remaining. The closest power of 2 to 1600 is 1024 (210). So the first person to go of the 1600 when there is 1024 people left will be the last person remaining. 1600 - 1024 = 576. 576 * 2 = 1152. Person 1152 will be the 576th person killed and person 1153 will be the first person to go of the remaining 1024 people.
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?
Answer: Cam can figure it out. If Dan saw that Cam and Butch had the same color hat he would know his hat color. Since he doesn't quickly figure out his hat color, Cam knows that him and Butch don't have the same hat color. So all he has to do is say that his hat color is the opposite of Butch's hat color (after giving enough time to be sure that Dan doesn't know his own color).
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