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FoolForMath
Group Title
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
 2 years ago
FoolForMath Group Title
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
 2 years ago

This Question is Closed

apoorvk Group TitleBest ResponseYou've already chosen the best response.0
Is it 7 by any chance?
 2 years ago

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

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

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

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

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

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

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

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

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

apoorvk Group TitleBest ResponseYou've already chosen the best response.0
dw:1338133822413:dw
 2 years ago

Ishaan94 Group TitleBest 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.
 2 years ago

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

apoorvk Group TitleBest ResponseYou've already chosen the best response.0
dw:1338134551987:dw
 2 years ago

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

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

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

TuringTest Group TitleBest 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...
 2 years ago

TuringTest Group TitleBest 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
 2 years ago

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

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

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

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

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

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.0
dw:1338137956244:dw
 2 years ago

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

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

apoorvk Group TitleBest 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?
 2 years ago

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

TuringTest Group TitleBest 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
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
...only diagonally
 2 years ago

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

TuringTest Group TitleBest 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
 2 years ago

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

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.0
dw:1338138315764:dw
 2 years ago

TuringTest Group TitleBest 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
 2 years ago

TuringTest Group TitleBest 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
 2 years ago

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

TuringTest Group TitleBest 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 ?
 2 years ago

apoorvk Group TitleBest 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".
 2 years ago

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

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

FoolForMath Group TitleBest 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/
 2 years ago

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

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
I agree :D
 2 years ago
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