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Is it 7 by any chance?
No, but it's a multiple of 7 ;)
make that 14.. or am i lolling myself again?
idk why but i feel it's 21.
I havent solved it yet, just a guess.
|dw:1338132939113:dw| need one more.
Why did the tiled square got deleted? It was helpful.
Now I will have to draw on my notebook :/
|dw:1338133230250:dw| Not so better than before!!
|dw:1338133213060:dw| okay 5 more - i learnt not to 'derive' answers lol.
Instead of 5, we can try three and four to get a generalized pattern. Counting isn't the right way.
For me at least. I keep messing up my count.
|dw:1338134999071:dw|i made a picture :)
...now somebody analyze it
I got 21 - and am pretty sure.
I'd like to show it though. I wanna figure a way to count based on the number of horizontal moves the mouse makes, like there is only 1 possible path with 5 moves horizontal|dw:1338135897949:dw|4 not possible... how many ways can he do it if he goes 3 horizontal steps?\ at least that's how I'm thinking...
|dw:1338136237586:dw|I see 3 possibilities along the bottom and one if he goes along the middle totaling 4 now it would be nice to find a pattern rather than count for 2
no, there are more... I made a mistake
That is what I drew above - the black lines are the movements along the grid.
I think you are right @apoorvk I just can't prove it
How do we know it's 21?
Are you sure of your counting?
The triangle doesnt trace this path.
what path is that o-0 ? it's all corner moves, right?
It's 21 for this - I am sure of this - checked that. How do we generalise this though?
What do you mean by corner move?
" In how many ways can the mouse reach the right lower corner vertex from the lower left corner vertex of the square" he can't start in the middle of a square, only a corner, so he cannot move vertically at all
" A mouse can leap along the diagonal or along the side of square tiles."
yeah, but try it if he makes a vertical move he will never reach the lower left corner
he's got to stay on the grid is the point I think
|dw:1338138438753:dw|" ...from the lower left corner vertex of the square " I took that to mean that he starts at this point|dw:1338138495546:dw|
and how is this|dw:1338138529062:dw|moving "along the edge of the tile"? I'd say that's moving through the middle of it
@FoolForMath is offline :/
he gave me a medal for my drawing, so I think that would mean I interpreted it correctly how did you read it @apoorvk ?
yeah ofcourse on the grid!! The instructions are pretty clear about that - it's about "vertex-to-vertex" jump, not from "spot-to-spot".
I see. I was doing it wrong all along :/ :( such a wasted effort :/
but that's great, now you can do it correctly for us @Ishaan94 :D
21 is the right answer. The general solution is also amazing :D Thanks to M.SE I found this one: http://en.wikipedia.org/wiki/Motzkin_number http://math.stackexchange.com/questions/150420/
lol ... that wasn't easy!! enlightening though!!
I agree :D