Difficult riddle about impatient people

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In summary, the two impatient people have agreed to meet between 3pm and 4pm near Nelson's Column in London, with a 15-minute waiting time. If they both arrive at a random time within the designated period, the probability of them meeting is 1/2. If they both strategically arrive between 3:15 and 3:45, the probability increases to 3/4. And if they both know the other's strategy and arrive around 3:30, the probability of them meeting is 1.
  • #1
americanpsy
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Two impatient people agree to meet up sometime between 3pm and 4 pm, in the era before mobile phones, just near Nelson's Column in London. They are so impatient they will only wait 15 minutes before leaving. What is the probability they actually meet up?
 
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  • #2
Supposing nobody will arrive before 3pm or after 4pm...
7/16
:smile:
 
  • #3
Yes that is the assumption. No arrivals before 3pm or after 4pm.
 
  • #4
An easy way to understand the answer...
 

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  • #5
If it is common knowledge that they will not arrive before 3 pm or after 4 pm, and wait for 15 minutes, they can do better: It is not necessary to show up before 3:15 - the other one will not have left before that. In the same way, it is not necessary to be there after 4 pm. Assuming that just one of them comes to that conclusion and the other one arrives at a random time, you can get a meeting probability of 1/2.
If both come to that conclusion, but choose a random arrival time between 3:15 and 3:45, their meeting probability is 3/4.
If they both know that the other one will do this analysis, they are both there around 3:30 and the meeting probability is 1.
 

Related to Difficult riddle about impatient people

1. What is the riddle about impatient people?

The riddle is about a group of impatient people who are trying to cross a bridge. The bridge can only hold two people at a time and each person takes a different amount of time to cross. The challenge is to figure out how the group can cross the bridge in the shortest amount of time.

2. How many people are involved in the riddle?

The riddle involves a group of five people who are trying to cross the bridge.

3. What is the solution to the riddle?

The solution is for the two slowest people to cross the bridge together, with one holding a flashlight to guide the way. Once they reach the other side, the person with the flashlight goes back and guides the other people across one by one. This way, the group can cross the bridge in a total of 17 minutes.

4. Why is this considered a difficult riddle?

This is considered a difficult riddle because it requires critical thinking and problem-solving skills. The answer is not immediately obvious and it may take several attempts to find the correct solution.

5. Are there any variations to this riddle?

Yes, there are variations to this riddle that involve different numbers of people, different crossing times, and different constraints. Some variations may have more than one solution, making it even more challenging.

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