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thts a lot of turns i can take x(

Kinda sounds like problem asked by FFM

who know when i could get lost :/ @Diyadiya will drive me! then no need to worry!

It is similar to FFM's problem.

then it must be related to this
http://en.wikipedia.org/wiki/Motzkin_number

n+1th Mozkin's no

@Ishaan94 i have an answer

o wait not yet!

|dw:1339345895603:dw|
seems to be six int this case

yes...six..\({4\choose 2}\)

maybe I should write it \[{2+2\choose 2}\]

|dw:1339346361572:dw|

|dw:1339346637952:dw|

so for 2x3 ...we have 10

\[{5 \choose 2}\]

so adding one segments ...
\[ \binom {4 + 1}{2}\]

\[{3+2\choose 2}\]

|dw:1339346850772:dw|

|dw:1339346924974:dw|

2*4+2*10+6*3 = \( \binom{9}{2} = \binom{3 + 3 + 3}{2}\)

there are only 20 ways for a 3x3

\[{m+n\choose n}\]

yes

isn't there 36 steps in 3x3??

show me a path that requires 36 steps

something wrong with draw app here ... can't copy my own drawing!!

only 6 steps are needed to get to the bottom right

|dw:1339348259654:dw|

there are 6 ways to do a 2x2 not 10

Oh .. i made mistake then ... it must be 3x2

|dw:1339348688431:dw|

yes

shouldn't it be 2*3*3+2*4+2*6 = 38 ??

try and draw 38 minimum distance paths using that graph

I'm getting ( m + n -2)!/(m-1)!(n-1)! ??????

|dw:1339384651187:dw|

My formula deals with streets. => lines.
=> m = 2, n=2 in this caase

mine does not