Question: If you have an 11 minute and 13 minute hourglass, how can you accurately time 15 minutes?
Answer: Start both hourglasses then when the 11 minute hourglass has finished immediately flip it again. When the 13 minute hourglass runs out the 11 minute hourglass will have 9 minutes left, so flip it and it will last another 2 minutes, 13 minutes + 2 minutes = 15 minutes.
Question: There are two ropes that both take exactly 1 hour to burn from end to end. You are unable to cut the rope. How can you burn the two ropes in a total of 45 minutes?
Answer: Start one of the ropes on fire from both ends and the other one from one end. After a half an hour one rope will be completely burnt and the other will be half burnt. At this point you light the final rope from the unlit side and it will take 15 minutes for the remaining half of the rope to burn, for a total of 45 minutes.
Question: A shrimping boat is at the docks with a lifeboat hanging off the side 5 meters above the water. If the tides rise at a rate of 1.5 meters per hour, how long would it take for the water to reach the lifeboat.
Answer: The entire shrimping boat would rise with the tides so the lifeboat would never be reached.
Question: How many people do you need to have the odds be in favor (at least 50% chance) of two people having the same birthday?
Answer: At least 23 people.
For an explanation visit http://en.wikipedia.org/wiki/Birthday_problem
Question: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a sports car; behind all of the others is bicycles. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 2, revealing a bicycle. He then says to you, "Do you want to pick door No. 3?" Is it to your advantage to switch your choice?
Answer: Yes, by changing your answer your chances of winning actually goes up from 1/3 to 2/3.
This becomes obvious when expanding the example. Suppose there was 100 doors rather than 3. You pick one and the host shows you that the car is not behind 98 of the doors then asks you to switch to the remaining door or keep the door you picked. Of course you would switch your door because chances are you didn't pick the correct door initially.
For more explanation go to http://en.wikipedia.org/wiki/Monty_Hall_problem#Solutions
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