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 2 years 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?
 2 years 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?

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FoolForMath
 2 years ago
Best ResponseYou've already chosen the best response.0No, but it's a multiple of 7 ;)

apoorvk
 2 years ago
Best ResponseYou've already chosen the best response.0make that 14.. or am i lolling myself again?

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0idk why but i feel it's 21.

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0I havent solved it yet, just a guess.

apoorvk
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1338132939113:dw need one more.

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0Why did the tiled square got deleted? It was helpful.

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0Now I will have to draw on my notebook :/

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1338133230250:dw Not so better than before!!

apoorvk
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1338133213060:dw okay 5 more  i learnt not to 'derive' answers lol.

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0Instead of 5, we can try three and four to get a generalized pattern. Counting isn't the right way.

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0For me at least. I keep messing up my count.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3dw:1338134999071:dwi made a picture :)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3...now somebody analyze it

apoorvk
 2 years ago
Best ResponseYou've already chosen the best response.0I got 21  and am pretty sure.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3I'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...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3dw: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

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3no, there are more... I made a mistake

apoorvk
 2 years ago
Best ResponseYou've already chosen the best response.0That is what I drew above  the black lines are the movements along the grid.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3I think you are right @apoorvk I just can't prove it

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0How do we know it's 21?

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0Are you sure of your counting?

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0The triangle doesnt trace this path.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3what path is that o0 ? it's all corner moves, right?

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

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0What do you mean by corner move?

TuringTest
 2 years ago
Best 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

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0" A mouse can leap along the diagonal or along the side of square tiles."

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

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3he's got to stay on the grid is the point I think

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

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

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0@FoolForMath is offline :/

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

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

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0I see. I was doing it wrong all along :/ :( such a wasted effort :/

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

FoolForMath
 2 years ago
Best ResponseYou've already chosen the best response.021 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/

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1lol ... that wasn't easy!! enlightening though!!
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