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Simple math question...

I

InlineFive

Diamond Member
Hey all,

I have a math question for you, yes it's a homework problem but I can't figure out the first portion.

There is a person who wants to visit 25 cities but take the shortest route between the cities and only visit each city once. How many possible routes are there?

25x25?

I can't get my brain around this...

Thanks.
 
first choice 1/25
second choice 1/24


etc...until you get to the 25th,

then calculate the possibilities for that entire string, and multiply it by 25.
 
Can you give us the name of the math class you're taking? The answer seems easy but the part "but take the shortest route between the cities" makes me cautious.
 
Are you saying 25^25? Can you explain that please?

Sorry, to clarify, visit all of the cities while keeping the total mileage to a minimum.
 
Originally posted by: Goosemaster
Originally posted by: OOBradm
you need to use permutations....

http://en.wikipedia.org/wiki/Permutation

In your case N=25, and R=25...

so the equation in the article simplifies to 25!, which should be your answer.
Click to expand...

aye...I new discrete would come into this.....question is, is he in discrete?


or algebra I or something😉
Click to expand...

I'm actually in College Algebra but math has never been my strong point. 🙁
 
Originally posted by: InlineFive
Originally posted by: Goosemaster
Originally posted by: OOBradm
you need to use permutations....

http://en.wikipedia.org/wiki/Permutation

In your case N=25, and R=25...

so the equation in the article simplifies to 25!, which should be your answer.
Click to expand...

aye...I new discrete would come into this.....question is, is he in discrete?


or algebra I or something😉
Click to expand...

I'm actually in College Algebra but math has never been my strong point. 🙁
Click to expand...



LOFL.....DIDN'T I SAY IT?!


Muwahahahahahah



<--da man😎


seriously though, n!, where n equals a number is called a factorial



5! for example, euqals 5x4x3x2x1 = 120

4! =4x3x2x1 = 24



Not that hard😀
 
25!

The reason: there are 25 ways to pick the first city, 24 ways to pick the next (because 1 has been eliminated), and 23 to pick the next (because 2 have been eliminated) etc.

25*24*23...*2*1 = 25!

For extra credit, come up with a simple way to find the shortest route without actually calculating the distances of all routes.

(shhhh...don't tell him the secret) 🙂
 
Originally posted by: pinion9
25!

The reason: there are 25 ways to pick the first city, 24 ways to pick the next (because 1 has been eliminated), and 23 to pick the next (because 2 have been eliminated) etc.

25*24*23...*2*1 = 25!

For extra credit, come up with a simple way to find the shortest route without actually calculating the distances of all routes.

(shhhh...don't tell him the secret) 🙂
Click to expand...

I have to

:evil:
 
Originally posted by: Goosemaster
first choice 1/25
second choice 1/24


etc...until you get to the 25th,

then calculate the possibilities for that entire string, and multiply it by 25.
Click to expand...

What exactly are you talking about? What does possibility have anything to do with the original question?

If randomly choosing a path, the probablity of picking the shortest path (assuming that all paths have different length) is simply 1/25!
 
Originally posted by: Goosemaster
I have to

:evil:
Click to expand...

No, I've seen this on TV before. We give him a question that hasn't been answered by the world's best mathematicians, tell him to solve it for homework, and he does. Then we are rich and he can quit mopping the floors.

 
Originally posted by: pinion9
Originally posted by: Goosemaster
first choice 1/25
second choice 1/24


etc...until you get to the 25th,

then calculate the possibilities for that entire string, and multiply it by 25.
Click to expand...

What exactly are you talking about? What does possibility have anything to do with the original question?

If randomly choosing a path, the probablity of picking the shortest path (assuming that all paths have different length) is simply 1/25!
Click to expand...

I was simply describing a route in terms of the entire possibility of rotues to perhaps, maybe, by chance, get him to udnerstand what is going on and not simply give him the answer


by 1 of 25 I meant that there are 25 possible choices for the first city, and then 24 possible choices for the nest city sicne you can't visit one twice.
 
Originally posted by: pinion9
Originally posted by: Goosemaster
I have to

:evil:
Click to expand...

No, I've seen this on TV before. We give him a question that hasn't been answered by the world's best mathematicians, tell him to solve it for homework, and he does. Then we are rich and he can quit mopping the floors.
Click to expand...


😀 LOL

Darn you guys...
 
Originally posted by: Chryso
Originally posted by: CombatChuk
25! (Factorial) maybe?
Click to expand...

Something like that.
Click to expand...

Yes, exactly that. But the real question is, do you understand why it is like that?

If you are given 25 cities to travel to, simply pick a city. How many cities can you possibly pick?

25

Okay, now you have picked a city (any city, it doesn't matter.) Now, how many cities can you pick from? There are only 24 left...

24

Now you have picked two cities. How many cities are left to pick from? 23...and so on.

You will eventually come down to a point where there is only one city left to choose from...

The reason you multiply them is because you can pick ANY of the cities for the first 25, and any of the remaining cities for the next 24, etc.

25*24*23....*2*1, which is commonly notated as 25! (pronounced 25 factorial)
 
Originally posted by: pinion9
Originally posted by: Chryso
Originally posted by: CombatChuk
25! (Factorial) maybe?
Click to expand...

Something like that.
Click to expand...

Yes, exactly that. But the real question is, do you understand why it is like that?

If you are given 25 cities to travel to, simply pick a city. How many cities can you possibly pick?

25

Okay, now you have picked a city (any city, it doesn't matter.) Now, how many cities can you pick from? There are only 24 left...

24

Now you have picked two cities. How many cities are left to pick from? 23...and so on.

You will eventually come down to a point where there is only one city left to choose from...

The reason you multiply them is because you can pick ANY of the cities for the first 25, and any of the remaining cities for the next 24, etc.

25*24*23....*2*1, which is commonly notated as 25! (pronounced 25 factorial)
Click to expand...


I'm glad I still remember my math skills!
 
Originally posted by: pinion9
Originally posted by: Goosemaster
I have to

:evil:
Click to expand...

No, I've seen this on TV before. We give him a question that hasn't been answered by the world's best mathematicians, tell him to solve it for homework, and he does. Then we are rich and he can quit mopping the floors.
Click to expand...

Since the probability of choosing the shortest path, mathematically, is not dependant on the characteristics of each individual path, since we assume to have none, it is simply based on the probability of choosing a certain path based on criterea that we do not have, do not know, and in this case, do not matter sicne thye will not influence our guess.


whatever the hell that means😛
 
Originally posted by: InlineFive
Originally posted by: pinion9
Originally posted by: Goosemaster
I have to

:evil:
Click to expand...

No, I've seen this on TV before. We give him a question that hasn't been answered by the world's best mathematicians, tell him to solve it for homework, and he does. Then we are rich and he can quit mopping the floors.
Click to expand...


😀 LOL

Darn you guys...
Click to expand...

HEY!:| MONEYTICKET! GET THE HELL BACK TO WORK BOI:|



*continues counting his accumulating stacks of $100s*
 
Originally posted by: ta8689
the answer is 25!
am i yelling or is it 25x24x23...etc ?
🙂
Click to expand...

It is, but the method of reaching that conclusion is a little more ellaborate than that.

edit: I see pinion9 acutally wrote it out😀
 
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