anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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apoorvk
  • apoorvk
Is it 7 by any chance?
anonymous
  • anonymous
No, but it's a multiple of 7 ;)
apoorvk
  • apoorvk
make that 14.. or am i lolling myself again?

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More answers

anonymous
  • anonymous
idk why but i feel it's 21.
anonymous
  • anonymous
I havent solved it yet, just a guess.
apoorvk
  • apoorvk
|dw:1338132939113:dw| need one more.
anonymous
  • anonymous
Why did the tiled square got deleted? It was helpful.
anonymous
  • anonymous
Now I will have to draw on my notebook :/
experimentX
  • experimentX
|dw:1338133230250:dw| Not so better than before!!
apoorvk
  • apoorvk
|dw:1338133213060:dw| okay 5 more - i learnt not to 'derive' answers lol.
apoorvk
  • apoorvk
BUGG!!!!^^
apoorvk
  • apoorvk
|dw:1338133822413:dw|
anonymous
  • anonymous
Instead of 5, we can try three and four to get a generalized pattern. Counting isn't the right way.
anonymous
  • anonymous
For me at least. I keep messing up my count.
apoorvk
  • apoorvk
|dw:1338134551987:dw|
TuringTest
  • TuringTest
|dw:1338134999071:dw|i made a picture :)
apoorvk
  • apoorvk
Cool^^
TuringTest
  • TuringTest
lol
TuringTest
  • TuringTest
...now somebody analyze it
apoorvk
  • apoorvk
I got 21 - and am pretty sure.
TuringTest
  • TuringTest
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...
TuringTest
  • TuringTest
|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
TuringTest
  • TuringTest
no, there are more... I made a mistake
apoorvk
  • apoorvk
That is what I drew above - the black lines are the movements along the grid.
TuringTest
  • TuringTest
I think you are right @apoorvk I just can't prove it
anonymous
  • anonymous
How do we know it's 21?
anonymous
  • anonymous
Are you sure of your counting?
anonymous
  • anonymous
|dw:1338137956244:dw|
anonymous
  • anonymous
The triangle doesnt trace this path.
TuringTest
  • TuringTest
what path is that o-0 ? it's all corner moves, right?
apoorvk
  • apoorvk
It's 21 for this - I am sure of this - checked that. How do we generalise this though?
anonymous
  • anonymous
What do you mean by corner move?
TuringTest
  • TuringTest
" 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
TuringTest
  • TuringTest
...only diagonally
anonymous
  • anonymous
" A mouse can leap along the diagonal or along the side of square tiles."
TuringTest
  • TuringTest
yeah, but try it if he makes a vertical move he will never reach the lower left corner
TuringTest
  • TuringTest
he's got to stay on the grid is the point I think
anonymous
  • anonymous
|dw:1338138315764:dw|
TuringTest
  • TuringTest
|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|
TuringTest
  • TuringTest
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
anonymous
  • anonymous
oh
anonymous
  • anonymous
@FoolForMath is offline :/
TuringTest
  • TuringTest
he gave me a medal for my drawing, so I think that would mean I interpreted it correctly how did you read it @apoorvk ?
apoorvk
  • 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".
anonymous
  • anonymous
I see. I was doing it wrong all along :/ :( such a wasted effort :/
TuringTest
  • TuringTest
but that's great, now you can do it correctly for us @Ishaan94 :D
anonymous
  • anonymous
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/
experimentX
  • experimentX
lol ... that wasn't easy!! enlightening though!!
anonymous
  • anonymous
I agree :D

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