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How many ways you can go from point A to point B

Network connection: Create a network that guides the signal from start to goalSignal-network: Create a network that guides 2 signalsHow many boxes are conductors?Regain your bearings from the logiciansLEVEL connectionsHow many boxes do you see?Hidden numbers (hand drawn)How many hourglasses can the madman find?

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2

1

$begingroup$

I know I have drawn the picture badly but can you tell how many ways we can go from point A to point B.

each path used once and no turning back...

visual

share|improve this question

edited 8 hours ago

Pʀıncess Anaya

asked 8 hours ago

Pʀıncess AnayaPʀıncess Anaya

9855 bronze badges

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  Infinite.$phantom!$
  $endgroup$
  – greenturtle3141
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Can the same point be visited more than once? Or each path used just once?
  $endgroup$
  – Weather Vane
  8 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @WeatherVane each path used once and there is no turning back...
  $endgroup$
  – Pʀıncess Anaya
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Well, this is classic combination math question :P
  $endgroup$
  – Conifers
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Conifers To be fair, counting paths on triangular grids can be a research-level mathematics problem.
  $endgroup$
  – Rand al'Thor
  6 hours ago
  

  
  
  
  

add a comment
 | 

2

1

$begingroup$

I know I have drawn the picture badly but can you tell how many ways we can go from point A to point B.

each path used once and no turning back...

visual

share|improve this question

edited 8 hours ago

Pʀıncess Anaya

asked 8 hours ago

Pʀıncess AnayaPʀıncess Anaya

9855 bronze badges

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  Infinite.$phantom!$
  $endgroup$
  – greenturtle3141
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Can the same point be visited more than once? Or each path used just once?
  $endgroup$
  – Weather Vane
  8 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @WeatherVane each path used once and there is no turning back...
  $endgroup$
  – Pʀıncess Anaya
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Well, this is classic combination math question :P
  $endgroup$
  – Conifers
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Conifers To be fair, counting paths on triangular grids can be a research-level mathematics problem.
  $endgroup$
  – Rand al'Thor
  6 hours ago
  

  
  
  
  

add a comment
 | 

$begingroup$

I know I have drawn the picture badly but can you tell how many ways we can go from point A to point B.

each path used once and no turning back...

visual

share|improve this question

edited 8 hours ago

Pʀıncess Anaya

asked 8 hours ago

Pʀıncess AnayaPʀıncess Anaya

9855 bronze badges

$endgroup$

share|improve this question

edited 8 hours ago

Pʀıncess Anaya

asked 8 hours ago

Pʀıncess AnayaPʀıncess Anaya

9855 bronze badges

share|improve this question

edited 8 hours ago

Pʀıncess Anaya

asked 8 hours ago

Pʀıncess AnayaPʀıncess Anaya

9855 bronze badges

asked 8 hours ago

Pʀıncess AnayaPʀıncess Anaya

9855 bronze badges

asked 8 hours ago

Pʀıncess AnayaPʀıncess Anaya

9855 bronze badges

3 Answers
3

active

oldest

votes

6

$begingroup$

My answer is below

Ans: 321
because there is only one way of getting to each of the points in a northerly direction, and also going direct
east

share|improve this answer

answered 8 hours ago

Sayed Mohd AliSayed Mohd Ali

4201414 bronze badges

$endgroup$

add a comment
 | 

1

$begingroup$

Assuming we can go only right and/or up, my answer is (as @SayedMohdAli's answer)

321

which was produced by this C code

#include <stdio.h>

#define MINGRID 2
#define MAXGRID 7

int grid;
int paths;

void recur(int x, int y)

 if(x == grid - 1 && y == grid - 1) 
 paths++;
 
 else if(x < grid && y < grid) 
 recur(x + 1, y);
 recur(x, y + 1);
 recur(x + 1, y + 1);
 


int main(void)

 for(grid = MINGRID; grid <= MAXGRID; grid++) 
 paths = 0;
 recur(0, 0);
 printf(">! grid=%d paths=%d n", grid, paths);
 

along with solutions for other sized grids:

grid=2 paths=3

grid=3 paths=13

grid=4 paths=63

grid=5 paths=321

grid=6 paths=1683

grid=7 paths=8989

and OEIS has this sequence A001850.

Central Delannoy numbers

3,13,63,321,1683,8989

Number of paths from (0,0) to (n,n) in an n X n grid using only steps north, northeast and east (i.e., steps (1,0), (1,1), and (0,1))

although I didn't look it up first!

There doesn't seem to be a clear and simple formula for it.

share|improve this answer

answered 7 hours ago

Weather VaneWeather Vane

6,08611 gold badge44 silver badges2424 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +1 for OEIS has this sequence Central Delannoy numbers
  $endgroup$
  – Sayed Mohd Ali
  5 hours ago
  
  

  
  
  
  

add a comment
 | 

0

$begingroup$

In a crude mathematical induction applied, I can

move in 3 ways, if there is one square, 31( 9diagonally + 11lateral) + 11lateral) ways, if there are 4 squares ... and so on...

And hence with

16 squares, it is 2^17 - 1 ways

share|improve this answer

edited 7 hours ago

answered 8 hours ago

Mea Culpa NayMea Culpa Nay

7,17411 gold badge77 silver badges4242 bronze badges

$endgroup$

add a comment
 | 

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6

$begingroup$

My answer is below

Ans: 321
because there is only one way of getting to each of the points in a northerly direction, and also going direct
east

share|improve this answer

answered 8 hours ago

Sayed Mohd AliSayed Mohd Ali

4201414 bronze badges

$endgroup$

add a comment
 | 

6

$begingroup$

My answer is below

Ans: 321
because there is only one way of getting to each of the points in a northerly direction, and also going direct
east

share|improve this answer

answered 8 hours ago

Sayed Mohd AliSayed Mohd Ali

4201414 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

My answer is below

Ans: 321
because there is only one way of getting to each of the points in a northerly direction, and also going direct
east

share|improve this answer

answered 8 hours ago

Sayed Mohd AliSayed Mohd Ali

4201414 bronze badges

$endgroup$

share|improve this answer

answered 8 hours ago

Sayed Mohd AliSayed Mohd Ali

4201414 bronze badges

answered 8 hours ago

Sayed Mohd AliSayed Mohd Ali

4201414 bronze badges

answered 8 hours ago

Sayed Mohd AliSayed Mohd Ali

4201414 bronze badges

1

$begingroup$

Assuming we can go only right and/or up, my answer is (as @SayedMohdAli's answer)

321

which was produced by this C code

#include <stdio.h>

#define MINGRID 2
#define MAXGRID 7

int grid;
int paths;

void recur(int x, int y)

 if(x == grid - 1 && y == grid - 1) 
 paths++;
 
 else if(x < grid && y < grid) 
 recur(x + 1, y);
 recur(x, y + 1);
 recur(x + 1, y + 1);
 


int main(void)

 for(grid = MINGRID; grid <= MAXGRID; grid++) 
 paths = 0;
 recur(0, 0);
 printf(">! grid=%d paths=%d n", grid, paths);
 

along with solutions for other sized grids:

grid=2 paths=3

grid=3 paths=13

grid=4 paths=63

grid=5 paths=321

grid=6 paths=1683

grid=7 paths=8989

and OEIS has this sequence A001850.

Central Delannoy numbers

3,13,63,321,1683,8989

Number of paths from (0,0) to (n,n) in an n X n grid using only steps north, northeast and east (i.e., steps (1,0), (1,1), and (0,1))

although I didn't look it up first!

There doesn't seem to be a clear and simple formula for it.

share|improve this answer

answered 7 hours ago

Weather VaneWeather Vane

6,08611 gold badge44 silver badges2424 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +1 for OEIS has this sequence Central Delannoy numbers
  $endgroup$
  – Sayed Mohd Ali
  5 hours ago
  
  

  
  
  
  

add a comment
 | 

1

$begingroup$

Assuming we can go only right and/or up, my answer is (as @SayedMohdAli's answer)

321

which was produced by this C code

#include <stdio.h>

#define MINGRID 2
#define MAXGRID 7

int grid;
int paths;

void recur(int x, int y)

 if(x == grid - 1 && y == grid - 1) 
 paths++;
 
 else if(x < grid && y < grid) 
 recur(x + 1, y);
 recur(x, y + 1);
 recur(x + 1, y + 1);
 


int main(void)

 for(grid = MINGRID; grid <= MAXGRID; grid++) 
 paths = 0;
 recur(0, 0);
 printf(">! grid=%d paths=%d n", grid, paths);
 

along with solutions for other sized grids:

grid=2 paths=3

grid=3 paths=13

grid=4 paths=63

grid=5 paths=321

grid=6 paths=1683

grid=7 paths=8989

and OEIS has this sequence A001850.

Central Delannoy numbers

3,13,63,321,1683,8989

Number of paths from (0,0) to (n,n) in an n X n grid using only steps north, northeast and east (i.e., steps (1,0), (1,1), and (0,1))

although I didn't look it up first!

There doesn't seem to be a clear and simple formula for it.

share|improve this answer

answered 7 hours ago

Weather VaneWeather Vane

6,08611 gold badge44 silver badges2424 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +1 for OEIS has this sequence Central Delannoy numbers
  $endgroup$
  – Sayed Mohd Ali
  5 hours ago
  
  

  
  
  
  

add a comment
 | 

$begingroup$

Assuming we can go only right and/or up, my answer is (as @SayedMohdAli's answer)

321

which was produced by this C code

#include <stdio.h>

#define MINGRID 2
#define MAXGRID 7

int grid;
int paths;

void recur(int x, int y)

 if(x == grid - 1 && y == grid - 1) 
 paths++;
 
 else if(x < grid && y < grid) 
 recur(x + 1, y);
 recur(x, y + 1);
 recur(x + 1, y + 1);
 


int main(void)

 for(grid = MINGRID; grid <= MAXGRID; grid++) 
 paths = 0;
 recur(0, 0);
 printf(">! grid=%d paths=%d n", grid, paths);
 

along with solutions for other sized grids:

grid=2 paths=3

grid=3 paths=13

grid=4 paths=63

grid=5 paths=321

grid=6 paths=1683

grid=7 paths=8989

and OEIS has this sequence A001850.

Central Delannoy numbers

3,13,63,321,1683,8989

Number of paths from (0,0) to (n,n) in an n X n grid using only steps north, northeast and east (i.e., steps (1,0), (1,1), and (0,1))

although I didn't look it up first!

There doesn't seem to be a clear and simple formula for it.

share|improve this answer

answered 7 hours ago

Weather VaneWeather Vane

6,08611 gold badge44 silver badges2424 bronze badges

$endgroup$

#include <stdio.h>

#define MINGRID 2
#define MAXGRID 7

int grid;
int paths;

void recur(int x, int y)

 if(x == grid - 1 && y == grid - 1) 
 paths++;
 
 else if(x < grid && y < grid) 
 recur(x + 1, y);
 recur(x, y + 1);
 recur(x + 1, y + 1);
 


int main(void)

 for(grid = MINGRID; grid <= MAXGRID; grid++) 
 paths = 0;
 recur(0, 0);
 printf(">! grid=%d paths=%d n", grid, paths);
 

share|improve this answer

answered 7 hours ago

Weather VaneWeather Vane

6,08611 gold badge44 silver badges2424 bronze badges

answered 7 hours ago

Weather VaneWeather Vane

6,08611 gold badge44 silver badges2424 bronze badges

answered 7 hours ago

Weather VaneWeather Vane

6,08611 gold badge44 silver badges2424 bronze badges

0

$begingroup$

In a crude mathematical induction applied, I can

move in 3 ways, if there is one square, 31( 9diagonally + 11lateral) + 11lateral) ways, if there are 4 squares ... and so on...

And hence with

16 squares, it is 2^17 - 1 ways

share|improve this answer

edited 7 hours ago

answered 8 hours ago

Mea Culpa NayMea Culpa Nay

7,17411 gold badge77 silver badges4242 bronze badges

$endgroup$

add a comment
 | 

0

$begingroup$

In a crude mathematical induction applied, I can

move in 3 ways, if there is one square, 31( 9diagonally + 11lateral) + 11lateral) ways, if there are 4 squares ... and so on...

And hence with

16 squares, it is 2^17 - 1 ways

share|improve this answer

edited 7 hours ago

answered 8 hours ago

Mea Culpa NayMea Culpa Nay

7,17411 gold badge77 silver badges4242 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

In a crude mathematical induction applied, I can

move in 3 ways, if there is one square, 31( 9diagonally + 11lateral) + 11lateral) ways, if there are 4 squares ... and so on...

And hence with

16 squares, it is 2^17 - 1 ways

share|improve this answer

edited 7 hours ago

answered 8 hours ago

Mea Culpa NayMea Culpa Nay

7,17411 gold badge77 silver badges4242 bronze badges

$endgroup$

share|improve this answer

edited 7 hours ago

answered 8 hours ago

Mea Culpa NayMea Culpa Nay

7,17411 gold badge77 silver badges4242 bronze badges

answered 8 hours ago

Mea Culpa NayMea Culpa Nay

7,17411 gold badge77 silver badges4242 bronze badges

answered 8 hours ago

Mea Culpa NayMea Culpa Nay

7,17411 gold badge77 silver badges4242 bronze badges