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The streets of a city are arranged like the lines of a chessboard. Let the dimensions be \(m \times n\). Find the number of ways in which a man can travel from the NorthWest corner to the SouthEast corner, going the shortest possible distance.
 one year ago
 one year ago
The streets of a city are arranged like the lines of a chessboard. Let the dimensions be \(m \times n\). Find the number of ways in which a man can travel from the NorthWest corner to the SouthEast corner, going the shortest possible distance.
 one year ago
 one year ago

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karatechopperBest ResponseYou've already chosen the best response.0
thts a lot of turns i can take x(
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Kinda sounds like problem asked by FFM
 one year ago

karatechopperBest ResponseYou've already chosen the best response.0
who know when i could get lost :/ @Diyadiya will drive me! then no need to worry!
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
It is similar to FFM's problem.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
then it must be related to this http://en.wikipedia.org/wiki/Motzkin_number
 one year ago

karatechopperBest ResponseYou've already chosen the best response.0
@Ishaan94 i have an answer
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1339345895603:dw seems to be six int this case
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
yes...six..\({4\choose 2}\)
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
maybe I should write it \[{2+2\choose 2}\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1339346361572:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1339346637952:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
so for 2x3 ...we have 10
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
so adding one segments ... \[ \binom {4 + 1}{2}\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1339346850772:dw
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
for your 3x2 you will have to go 3 units up and 2 units to the right in total to get to the upper right hand corner UUURR the number of ways to arrange these letters is \({3+2\choose 2}\)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1339346924974:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
2*4+2*10+6*3 = \( \binom{9}{2} = \binom{3 + 3 + 3}{2}\)
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
there are only 20 ways for a 3x3
 one year ago

goxenulBest ResponseYou've already chosen the best response.0
Yeah, because you take m+n steps and you must decide which n of them will be right, or which m of them will be down (it's equivalent).
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
isn't there 36 steps in 3x3??
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
show me a path that requires 36 steps
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
something wrong with draw app here ... can't copy my own drawing!!
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
only 6 steps are needed to get to the bottom right
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1339348259654:dw
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
there are 6 ways to do a 2x2 not 10
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Oh .. i made mistake then ... it must be 3x2
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1339348688431:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
shouldn't it be 2*3*3+2*4+2*6 = 38 ??
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
try and draw 38 minimum distance paths using that graph
 one year ago

siddhantsharanBest ResponseYou've already chosen the best response.1
I'm getting ( m + n 2)!/(m1)!(n1)! ??????
 one year ago

siddhantsharanBest ResponseYou've already chosen the best response.1
dw:1339384651187:dw
 one year ago

siddhantsharanBest ResponseYou've already chosen the best response.1
Let each square formed be a unit square. Therefore if a man needs to get from NW to south east, He basically needs to cover "n1" units on the east line. And "m1" units south.  For the Shortest possible path when he decides to never turn back. Now in order to do this each street taken by him must be in the South or east direction. Every time he goes east Lets call that turn/ street taken E. Every time he turns south we call that S. So any path followed by him can be written as: SSESESESSSSEEE...........  Meaning the man goes first south then south again without turning at next intersection Then turns east at the next turn.......... Here number of S's = m1 No. of E's = n1. So the problem has become an equivilant of Finding the permutations of n1 E's and m1 S's. = ( m 1 + n 1)!  (m1)!(n1)!
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
dw:1339422624581:dw this is a 1x1 block so m=1 and n=1 using your formula \[\frac{(11+11)}{(11)!(11)!}=\frac{0!}{0!0!}=1\] but there are 2 paths to the end
 one year ago

siddhantsharanBest ResponseYou've already chosen the best response.1
My formula deals with streets. => lines. => m = 2, n=2 in this caase
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
I go by the number of blocks created and the number of steps to go from one corner to the other for a 1x1 block you have to go down 1 and to the right 1
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
should have never doubted @Zarkon http://math.stackexchange.com/questions/103470/howcanifindthenumberoftheshortestpathsbetweentwopointsona2dlatti
 one year ago
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