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: You have a glass of water that looks about half full. How can you tell, only using the glass of water itself, if the glass is half full or not?
The glass is a right cylinder.
Answer: Tip the glass of water until the water reaches the rim of the glass and if the water lines up perfectly with the bottom rim of the glass, it is half full.
Question: If you have 30 white socks, 22 black socks, and 14 blue socks scattered across the floor in the dark, how many would you have to grab to get a matching pair?
Answer: 4. Once you grab 4 you will definitely have 2 of the same color.
Question: There are 100 passengers boarding a 100 passenger airplane. When passenger 1 gets onto the plane, he is dissoriented, so he randomly picks a seat. Each of the remaining passengers (2, 3, 4, etc.) get onto the plane and take their seat if it is available or picks one of the remaining seats at random if it is not.
What is the chance that the last passenger (passenger 100) will get his seat?
Answer: There is a 50 percent chance.
When the last passenger gets on seats 2 - 99 will be taken for sure. Each of these passengers would take their seats if they were available, so the only seat remaining at the end would be 1 or 100. So there is a 50 percent chance that passenger 100 would get seat 100.
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