#3**+10 **

Mmm Well there are 4 ways to get from E to F

Now going from F to G

If you horizontal first then there are 4 ways

if you go down1 then across there are 3 ways

if you go down 2 then across there ae 2 ways

if you go all the way down first then there is 1 way.

4+3+2+1=10 ways

If that is correct then there would be 4*10=40 ways to go from E to F to G

Melody
Apr 2, 2015

#2**+10 **

The ways to get from E to F = [1 + 3] ! / [1! * 3!] = 4!/3! = 4 ways

Ways to get from F to G = [3 + 2]! / [3! * 2! ] = 5! / 12 = 120 / 12 = 10 ways

So

4 ways x 10 ways = 40 ways to go from E to G through F

CPhill
Apr 2, 2015

#3**+10 **

Best Answer

Mmm Well there are 4 ways to get from E to F

Now going from F to G

If you horizontal first then there are 4 ways

if you go down1 then across there are 3 ways

if you go down 2 then across there ae 2 ways

if you go all the way down first then there is 1 way.

4+3+2+1=10 ways

If that is correct then there would be 4*10=40 ways to go from E to F to G

Melody
Apr 2, 2015

#5**+5 **

I actually can't take much credit for this one.......the answer comes straight from a "formula" supplied by Nauseated....

For any R x C grid arrangement where R represents the rows and C represents the columns.....the number of distinct paths from one corner of the grid to a diagonally opposite corner is given by :

(R + C ) ! / [R! * C! ]

CPhill
Apr 2, 2015

#6**+5 **

Minimum amount of steps E -> F -> G is 8, but 9 steps is required.

I.e. E -> F in 4 steps & F -> G in 5 steps, or E -> F in 5 steps & F -> G in 4 steps.

So is 40 ways to go from E to F to G in **8 **steps, or did you somehow take that additional step into account?

(I don't have spare time to calculate, so cannot check this.. so just wondering)

Guest Apr 2, 2015

#7**+5 **

Hi anon, thanks for getting involved - we like that.

However, the minimum number is 9. 5 across and 4 down

I don't know where you got 8 from? :)

Hi Chris,

Yes i thought that might be Nauseated's formula, It is nifty,

There are so many formuas for so many things i cannot remember them all.

I suppose i should try and organise a file for some of these new ones.

Melody
Apr 2, 2015