Seems quiet tonight, so...

[Silly Sausage]

Given a chessboard (8 x 8 square grid) and a piece which is only allowed to move one square upwards or rightwards (it cannot move diagonally, downwards or left).

The piece starts in the bottom left corner of the board and you have to move it to the top right corner. There are clearly lots of ways to do this, and they all require 14 moves.

The question is: Exactly how many different paths may be taken by this piece to get from the bottom left corner of the board to the top right?


No googling!

 

[SPARTYKUS]

Are you in Mensa?

 

[Guest77]

paths which involve 14 moves or any amount of moves?

 

[Guest77]

Are you in Mensa?

No Manchester chuckle

 

[Richard Burns]

If you start with you can go up 8 and then right 8 or you could go right 8 and then up 8 and there are 8 different ways of describing the change from one to the other. i.e. up 7 then right 8 then up 1 and so on.
I am then tempted to say that you can only describe eight other starting paths and so the choices are 64 paths.
However I feel I have missed some options as I may be only considering left to right and not also considering bottom to top so I will go with 512 (64 X 8) paths.

However this does assume that you are considering the first and last moves as part of the path otherwise it gets too complicated for me.

 

[dingledong]

I really mean it this time

GASP

 

[telectrix]

if you put 2 grains of rice on the 1st square of a chess board, then 4 on the 2nd, 8 on the 3rd, and so on till you got to the last square, what would you have ( apart from a heavy chess board )?

 

[Knobhead]

1.94467E[SUP]19 [/SUP]Grains

No I’m not working it out in to tons.

 

[Bobster]

About 210 billion tons.

 

[Guest55]

Given a chessboard (8 x 8 square grid) and a piece which is only allowed to move one square upwards or rightwards (it cannot move diagonally, downwards or left).

The piece starts in the bottom left corner of the board and you have to move it to the top right corner. There are clearly lots of ways to do this, and they all require 14 moves.

The question is: Exactly how many different paths may be taken by this piece to get from the bottom left corner of the board to the top right?


No googling!

so what was the answer then ?

i had a small ponder with my own chess board , couldnt decide between 2 numbers , 1 small and 1 big.

 

[D Skelton]

if you put 2 grains of rice on the 1st square of a chess board, then 4 on the 2nd, 8 on the 3rd, and so on till you got to the last square, what would you have ( apart from a heavy chess board )?

More grains of rice than could be grown by all the world's rice growers in a thousand years!

 

[davesparks]

So we've all seen that particular episode of QI then!

 

[HappyHippyDad]

Just seen this Archy! I like these sort of things... get a bit carried away with them though!! You find a pattern and then follow it through. I'm not sure if its right as I just cant find an equation that links all the diagonals together to check it, which is very frustrating!!!

I should be able to see how 0, 2, 6, 20, 70, 252, 924, 3432 are formed without just adding the previous 2 figures but I cant see the equation which makes me think it might be wrong!!!



Should explain the above a bit more!

If it were a 2 x 2 board (see small diagram) there would be 2 moves to get to top right.
If 3 x 3 , there would be 6 different ways of getting to top right.
If 4 x 4, there would be 20 ways etc etc.
So an 8 x 8 board has 3432 variations of the move stated.

You can see from diagram that to get this figure you add the figure above it and to the right, but this is not very scientific and would not enable you to find the number of moves it would take on a N x N board.

Its something to do with N-1 or 2 to the power of N-1 or N! (factorial) but I cant see it! Enjoying working it out though Archy, thanks :smile5:

 

[Silly Sausage]

Good effort HHD!!!

The answer is 3432.

You can think this out...
There are 14 moves, 7 of which are either up or right.
So it's a simple Combination of 7 out of 14, [SUP]14[/SUP]C[SUB]7[/SUB] = 3432.

 

[HappyHippyDad]

Good effort HHD!!!

The answer is 3432.

You can think this out...
There are 14 moves, 7 of which are either up or right.
So it's a simple Combination of 7 out of 14, [SUP]14[/SUP]C[SUB]7[/SUB] = 3432.

!!!!! Of course!!!

Its 14C7 = [n!/((n-k)! x k!)]

Where n=14 k=7

therefore

= 14!/((14-7)! x 7!)

= 14x13x12x11x10... etc / ((7x6x5...)x(7x6x5...))

= 3432.

I should have seen that! I was getting too carried away with the number of squares down each side rather than the combinations.

Thanks again Archy, I used to enjoy all that stuff (statistics) and haven't done it since school.

 

[dingledong]

Just what I was thinking



Not

 

[Silly Sausage]

I used to enjoy all that stuff (statistics)

I was starting to like you...but enjoying statitics...you've crossed a line there!

 

[dingledong]

You started it archy