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By gandalf

Question: Two men find an old gold coin and want to have a coin toss with it to decide who gets it. The only problem is the coin is heavier on one side so it comes up heads more than tails. What is a fair way for the men to toss the coin and decide who gets the coin?

Answer: They just have to flip it twice. They call the first toss either heads or tails, then the next toss they automatically pick the opposite (ie if one man calls heads on the first flip, he automatically picks tails on the second and vice versa). If they both win one toss (a tie) out of the two, they just have to repeat until one of them wins both tosses.

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Question: John has been hired to paint the numbers 1 through 100 on 100 apartments.

How many times with he have to paint 8?

Answer: 20 times. (8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 98).

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Question: A claustrophobic person gets on a train. The train enters a tunnel just as it is leaving the station.

Where is the best place for him to sit?

Answer: In the back. The train will be accelerating so it will be going faster when the back of the train enters the tunnel so a person in the back will spend less time in the tunnel.

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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.

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Question: Why does the second shape have an open block when the first shape does not?

Answer: The two triangles have different slopes so in the second shape the two triangles cause the shape to bulge out to account for the extra square unit.

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