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  RE: A gas station problem  
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Kenny Ruff
Posts : 15 Join date : 20100628
 Subject: RE: A gas station problem 7/1/2010, 17:55  
 At what point did you say that there could not be only 1 gas station?
My point is that you begin your trip with an empty "car gas tank" and then fill your "car gas tank" thus leaving the "station gas tank" empty, thus leaving one empty tank remaining.
Now, with the gas from that one gas station, as in your puzzle above, there will be just enough to traverse the circle.
In my solution, there are NOT 2 gas stations, nor will there be. In my solution, there is only 1, as you said "any number of gas stations".
My solution will not be compared to another solution with entirely different logic.
My point still stands. 
   TheSleepingDragon
Posts : 65 Join date : 20100626
 Subject: Re: RE: A gas station problem 7/1/2010, 19:11  
 Here is the original statement of the question:
Prove that for any number of gas stations arranged on a circular track such that all the gas stations combined have just enough gas to get you all the way around the circle that there must exist a valid gas station that you can start at with an empty tank and go all the way around the circle.
Mathematicians commonly refer to the words "for any number" as solving for the case n. In this manner, any singular case of n=a where a is some constant is considered not mathematically acceptable. This is because in mathematics the concept "for any" is considered equivalent to the concept "for all". I quite apologize if I did not make that clear, and I do acknowledge that your solution works for the case n = 1.
That does not change the fact that you did not solve the original question in a manner acceptable to the mathematical community. As such, I must continue to insist that you have still not solved the problem. 
   Kenny Ruff
Posts : 15 Join date : 20100628
 Subject: Re: RE: A gas station problem 7/1/2010, 22:17  
 If n = a, and for the purpose of trail and error, as is repetitive in mathematics, if a = 1, then the problem can be solved by a equalling 1. Therefore, no matter how you look at this problem, 1 is a possible solution. I am not saying that this is the only solution, but it is definitely a valid solution, and there is no way around that. 
   TheSleepingDragon
Posts : 65 Join date : 20100626
 Subject: Re: RE: A gas station problem 7/1/2010, 23:22  
 Yes. It is true that your solution for n=1 is valid. That is, you have provided a solution for a very singular case.
However I would like to, again, point out that you have not shown a solution that works for every case. There are, of course, an infinity of cases to consider. N=0, 2, 9, 11, 23522123, etc. Since, mathematically speaking, I asked for a solution "for any number of gas stations" and that is mathematically equivalent to "for all possible numbers of gas stations", I must regrettably insist that you have not solved the problem. It's rather sad that I must, because I find your solution for the case of n=1 quite imaginative and clever. However, my original request remains the same: find a solution that works for every possible case. 
   Kenny Ruff
Posts : 15 Join date : 20100628
 Subject: Re: RE: A gas station problem 7/2/2010, 00:55  
 I hate to break it to you...but ESPECIALLY in mathetmatics, rarely is there only one solution to any given problem. I am glad to hear that you have accepted my solution as one possible solution, but I will still firmly say that you have no grounds to be saying anything negative about my solution. You should be like a genuine questionasker, and accept answers/solutions with an open mind, instead of criticizing all that are given, and then trying to complicate matters. Stick with yout original question. If you would like to propose a different problem, then post another topic, or gladly accept the current solution given, and then note that you are changing the terms, and ask your new, yet similar question/puzzle. In any case, this has been a relatively interesting puzzle, but my solution has been given, and others that visit this puzzle are welcome to elaborate upon it.
Good day sir,
Kenny 
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