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Just another super easy problem,
A \( 5\times 5 \) square is made of square tiles of dimensions \( 1\times 1 \). A mouse can leap along the diagonal or along the side of square tiles. In how many ways can the mouse reach the right lower corner vertex of the square from the lower left corner vertex of the square leaping exactly \(5\) times?
 one year ago
 one year ago
Just another super easy problem, A \( 5\times 5 \) square is made of square tiles of dimensions \( 1\times 1 \). A mouse can leap along the diagonal or along the side of square tiles. In how many ways can the mouse reach the right lower corner vertex of the square from the lower left corner vertex of the square leaping exactly \(5\) times?
 one year ago
 one year ago

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apoorvkBest ResponseYou've already chosen the best response.0
Is it 7 by any chance?
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.0
No, but it's a multiple of 7 ;)
 one year ago

apoorvkBest ResponseYou've already chosen the best response.0
make that 14.. or am i lolling myself again?
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
idk why but i feel it's 21.
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
I havent solved it yet, just a guess.
 one year ago

apoorvkBest ResponseYou've already chosen the best response.0
dw:1338132939113:dw need one more.
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
Why did the tiled square got deleted? It was helpful.
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
Now I will have to draw on my notebook :/
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1338133230250:dw Not so better than before!!
 one year ago

apoorvkBest ResponseYou've already chosen the best response.0
dw:1338133213060:dw okay 5 more  i learnt not to 'derive' answers lol.
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
Instead of 5, we can try three and four to get a generalized pattern. Counting isn't the right way.
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
For me at least. I keep messing up my count.
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
dw:1338134999071:dwi made a picture :)
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
...now somebody analyze it
 one year ago

apoorvkBest ResponseYou've already chosen the best response.0
I got 21  and am pretty sure.
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
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 horizontaldw:1338135897949:dw4 not possible... how many ways can he do it if he goes 3 horizontal steps?\ at least that's how I'm thinking...
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
dw:1338136237586:dwI 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
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
no, there are more... I made a mistake
 one year ago

apoorvkBest ResponseYou've already chosen the best response.0
That is what I drew above  the black lines are the movements along the grid.
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
I think you are right @apoorvk I just can't prove it
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
How do we know it's 21?
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
Are you sure of your counting?
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
dw:1338137956244:dw
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
The triangle doesnt trace this path.
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
what path is that o0 ? it's all corner moves, right?
 one year ago

apoorvkBest ResponseYou've already chosen the best response.0
It's 21 for this  I am sure of this  checked that. How do we generalise this though?
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
What do you mean by corner move?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
" 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
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
" A mouse can leap along the diagonal or along the side of square tiles."
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
yeah, but try it if he makes a vertical move he will never reach the lower left corner
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
he's got to stay on the grid is the point I think
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
dw:1338138315764:dw
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
dw:1338138438753:dw" ...from the lower left corner vertex of the square " I took that to mean that he starts at this pointdw:1338138495546:dw
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
and how is thisdw:1338138529062:dwmoving "along the edge of the tile"? I'd say that's moving through the middle of it
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
@FoolForMath is offline :/
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
he gave me a medal for my drawing, so I think that would mean I interpreted it correctly how did you read it @apoorvk ?
 one year ago

apoorvkBest ResponseYou've already chosen the best response.0
yeah ofcourse on the grid!! The instructions are pretty clear about that  it's about "vertextovertex" jump, not from "spottospot".
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
I see. I was doing it wrong all along :/ :( such a wasted effort :/
 one year ago

TuringTestBest ResponseYou've already chosen the best response.3
but that's great, now you can do it correctly for us @Ishaan94 :D
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.0
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/
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
lol ... that wasn't easy!! enlightening though!!
 one year ago
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