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The bus is late: Have you ever wondered whether you should start walking or whether it was better to wait?
Or, when it is raining, what COA will wet you less: Walking or running?
Similar probs and more (...what curve in time would a light bulb on your head produce if you walked though the center of London, and how would it differ from walking in N.Y?) + great Haikus are discussed in one of my favorite books ever, "Cryptonomicon" by Neal Stephenson (first chapter in English here: http://www.cryptonomicon.com/text.html), but at least the first one is now solved:
New Scientist has an article about it:
http://www.newscientist.com/article/...r-the-bus.html
Lazy option is best when waiting for the bus
Quote: 23 January 2008: Ever lose patience waiting for a bus and decided to walk instead? Next time, stick around, it's nearly always the best strategy.
Scott Kominers, a mathematician at Harvard University, and his colleagues derived a formula for the optimal time that you should wait for a tardy bus at each stop en route before giving up and walking on. "Many mathematicians probably ponder this on their way to work, but never get round to working it out," he says.
The team found that the solution was surprisingly simple. When both options seem reasonably attractive, the formula advises you to choose the "lazy" option: wait at the first stop, no matter how frustrating (www.arxiv.org/abs/0801.0297).
The formula does break down in extreme cases, Kominers says, when the time interval between buses is longer than an hour, for example, and your destination is only a kilometre away.
If you do choose to walk, you should make your decision before you start waiting, he says. You will still reach your destination later than the bus you'd have caught, but it will be much less frustrating than waiting for a while and then watching the bus shoot by. "It certainly has changed the way I travel," Kominers says.
Which reminds me of a riddle that took me long time to solve, can you? :
- Zack lives in a house that has two bus stops in front of it, one for A-Bus and one for B-Bus.
- A-Bus always and exclusively goes to A-Twon from this bus stop
- B-Bus always and exclusively goes to B-Twon from this bus stop
- Both A- and B-bus pass their respective bus stop precisely once every hour 24 hours a day, 7 days a week
Now, Zack - as almost every male - has two girl friends he is equally madly in love with: Amy in A-town and Betty in B-town.
Being a man of good intentions he leaves the decision whom of the two to meet to destiny and leaves is house at (mathematically) random times once a day to take the next coming bus to whichever town it takes him, and then stays with the girl there for a few hours.
He repeats this for 100 days, and, after consulting his diary, finds out - to his surprise (he had expected to distribute his visits about evenly between Amy and Betty) - that he had ended up 20x in A-Town in this period, but 80x in B-town.
How come?
Rattler
Or, when it is raining, what COA will wet you less: Walking or running?
Similar probs and more (...what curve in time would a light bulb on your head produce if you walked though the center of London, and how would it differ from walking in N.Y?) + great Haikus are discussed in one of my favorite books ever, "Cryptonomicon" by Neal Stephenson (first chapter in English here: http://www.cryptonomicon.com/text.html), but at least the first one is now solved:
New Scientist has an article about it:
http://www.newscientist.com/article/...r-the-bus.html
Lazy option is best when waiting for the bus
Quote: 23 January 2008: Ever lose patience waiting for a bus and decided to walk instead? Next time, stick around, it's nearly always the best strategy.
Scott Kominers, a mathematician at Harvard University, and his colleagues derived a formula for the optimal time that you should wait for a tardy bus at each stop en route before giving up and walking on. "Many mathematicians probably ponder this on their way to work, but never get round to working it out," he says.
The team found that the solution was surprisingly simple. When both options seem reasonably attractive, the formula advises you to choose the "lazy" option: wait at the first stop, no matter how frustrating (www.arxiv.org/abs/0801.0297).
The formula does break down in extreme cases, Kominers says, when the time interval between buses is longer than an hour, for example, and your destination is only a kilometre away.
If you do choose to walk, you should make your decision before you start waiting, he says. You will still reach your destination later than the bus you'd have caught, but it will be much less frustrating than waiting for a while and then watching the bus shoot by. "It certainly has changed the way I travel," Kominers says.
Which reminds me of a riddle that took me long time to solve, can you? :
- Zack lives in a house that has two bus stops in front of it, one for A-Bus and one for B-Bus.
- A-Bus always and exclusively goes to A-Twon from this bus stop
- B-Bus always and exclusively goes to B-Twon from this bus stop
- Both A- and B-bus pass their respective bus stop precisely once every hour 24 hours a day, 7 days a week
Now, Zack - as almost every male - has two girl friends he is equally madly in love with: Amy in A-town and Betty in B-town.
Being a man of good intentions he leaves the decision whom of the two to meet to destiny and leaves is house at (mathematically) random times once a day to take the next coming bus to whichever town it takes him, and then stays with the girl there for a few hours.
He repeats this for 100 days, and, after consulting his diary, finds out - to his surprise (he had expected to distribute his visits about evenly between Amy and Betty) - that he had ended up 20x in A-Town in this period, but 80x in B-town.
How come?
Rattler
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