Problem 371
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Problem 371
Are the letters restricted to uppercase?
Does Seth reckon in his own license plate? For example, suppose Seth's license plate is SET001, when he saw CAT999, is this a win?
Does Seth reckon in his own license plate? For example, suppose Seth's license plate is SET001, when he saw CAT999, is this a win?
Re: Problem 371
Note: You may assume each licence plate seen is equally likely to have any three digit number on it.
Does that matter?greedp wrote:Are the letters restricted to uppercase?
Do you see your licence plate when driving?Does Seth reckon in his own license plate? For example, suppose Seth's license plate is SET001, when he saw CAT999, is this a win?
Re: Problem 371
000 is a valid license plate number.LarryBlake wrote:Is 000 valid?
Re: Problem 371
So why isn't this just a Bernoulli random variable with p = 999 / 1000000?

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Re: Problem 371
I was thinking that this would be Geometric, but that doesn't seem to be the case either for one reason or another.
Re: Problem 371
It's not a Bernoulli random variable because p depends on what happened in the previous trials.Nadando wrote:So why isn't this just a Bernoulli random variable with p = 999 / 1000000?
Re: Problem 371
I am thoroughly confused by the note and also the update by hk above. Is it valid to see the same license plate multiple times (as it can happen in real life on the highways )? If so, for example, SET500 and SET500 will be a win. Right?
puzzle is a euphemism for lack of clarity
Re: Problem 371
Right. Even if it's XYZ500 and ABC500, or any other letter combinations.If so, for example, SET500 and SET500 will be a win. Right?
From the problem description,
As hk implied, you never see your own plate while on the road. (And, even if you did, it would still be one of the expected number if you consider it as a random 3digit plate.)expected number of plates he needs to see for a win
When you assume something, you risk being wrong half the time.
Re: Problem 371
SET500 and SET500 is same car twice
XYZ500 and ABC500 is two separate cars
By saying "you consider it as a random 3digit plate" are you implying to ignore the letters? Which is related to hk's comment "Does that matter?" for considering upper/lowercase letters. Ignoring letters will alter the distribution.
XYZ500 and ABC500 is two separate cars
By saying "you consider it as a random 3digit plate" are you implying to ignore the letters? Which is related to hk's comment "Does that matter?" for considering upper/lowercase letters. Ignoring letters will alter the distribution.
puzzle is a euphemism for lack of clarity
Re: Problem 371
I have to admit that you may have a point there IF they are both Oregon plates. And in heavy traffic, you could see it numerous times, specially if it's on the car in front of you. But, with a bit of imagination, numerous other scenarios could be elaborated (albeit not in this thread).SET500 and SET500 is same car twice
From the problem statement,
maybe the two should have been underlined and then explained/qualified in considerably more detail.Whenever the numbers of two licence plates seen on his trip
Any suggestion?
When you assume something, you risk being wrong half the time.
Re: Problem 371
Yes.rayfil wrote:I have to admit that you may have a point there IF they are both Oregon plates. And in heavy traffic, you could see it numerous times, specially if it's on the car in front of you. But, with a bit of imagination, numerous other scenarios could be elaborated (albeit not in this thread).SET500 and SET500 is same car twice
From the problem statement,maybe the two should have been underlined and then explained/qualified in considerably more detail.Whenever the numbers of two licence plates seen on his trip
Any suggestion?
Add the note:
Note: You may assume each licence plate seen is equally likely to have any three digit number on it.
I fear that explaining in considerable more detail makes an otherwise nice problem almost unreadable.
Re: Problem 371
The note:sivakd wrote:SET500 and SET500 is same car twice
XYZ500 and ABC500 is two separate cars
By saying "you consider it as a random 3digit plate" are you implying to ignore the letters? Which is related to hk's comment "Does that matter?" for considering upper/lowercase letters. Ignoring letters will alter the distribution.
Note: You may assume each licence plate seen is equally likely to have any three digit number on it.
tells you exactly to ignore the letters and also to ignore other so called "literate" attempts to make the problem more difficult than was meant.Re: Problem 371
I think the word "may" should be changed to "must" or "should". It's imperative to get the answer, unlike (for example) problem 177 which states:hk wrote:Note: You may assume each licence plate seen is equally likely to have any three digit number on it.tells you exactly to ignore the letters and also to ignore other so called "literate" attempts to make the problem more difficult than was meant.
Note: In your calculations you may assume that a calculated angle is integral if it is within a tolerance of 10^{9} of an integer value.
which I take as an optional suggestion.Re: Problem 371
I finally solved this and hopefully no one would object if I write the statement "ignore that the license plates have letters completely, just assume there are 3 digit license plates and many cars can have the same 3 digits such that the probability of seeing any number is the same for any i^{th} car seen". It may be same as the Note: provided in the problem, but for people who have difficulty understanding the note ...
puzzle is a euphemism for lack of clarity
Re: Problem 371
Seeing the troubles some people have had I changed the note into
Doing as if there are exactly 26^3*1000 cars moving around is as doubtful an assumption as nobody can assure that exactly all licence plates have been handed out and that e.g. some that were handed out long ago aren't in use any more.
We assume that each licence plate seen is equally likely to have any three digit number on it.
This is according to the same strategy as used in Problem 317 (View Problem) where is stated :
We assume that the fragments move without air resistance...
I doubt that firecrackers can be launched in vacuum and the gravitational field of the earth (or whichever celestial body) is far from uniform.Doing as if there are exactly 26^3*1000 cars moving around is as doubtful an assumption as nobody can assure that exactly all licence plates have been handed out and that e.g. some that were handed out long ago aren't in use any more.
Re: Problem 371
States definitely use nonrandom methods to generate the license plates; for example, letter combinations that might be offensive or politically charged are suppressed.
Re: Problem 371
Can someone explain the best way to go about a problem like this? Is this more paperandpencil than it is programming? Obviously a simple simulation would take way to long to get the accuracy required, right? There are plenty more of these "simulation"type problems on ProjectEuler where, given enough time, a simulation would work (I think) although that clearly isn't the most efficient way of doing it. What principals are at play here?
Re: Problem 371
Paper & Pencil can be used to come up with some formulas but you would need a computer to crunch the numbers. At least an Excel would come handy. Writing simulation usually helps validate whether the formulas are in the right direction or not as it did in my case. I wouldn't recommend running simulation for a long time till you arrive at the desired precision or close to it and testing out a few values. That would defeat the purpose of solving these type of problems.
puzzle is a euphemism for lack of clarity
Re: Problem 371
That makes sense. What level of Math do you think the "average" person would need to complete a problem like 371? Is it even remotely possible for someone with just Calculus II knowledge and a bit of Linear Algebra to solve a problem like this? (I'm a college freshmen, but these problems intrigue me so much!!)Paper & Pencil can be used to come up with some formulas but you would need a computer to crunch the numbers. At least an Excel would come handy. Writing simulation usually helps validate whether the formulas are in the right direction or not as it did in my case. I wouldn't recommend running simulation for a long time till you arrive at the desired precision or close to it and testing out a few values. That would defeat the purpose of solving these type of problems.