Problem 44066. Number of paths on a 3d grid

Created by Jihye Sofia Seo

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This problem is inspired by</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/1483-number-of-paths-on-a-grid\"><w:r><w:t>&lt;https://www.mathworks.com/matlabcentral/cody/problems/1483-number-of-paths-on-a-grid</w:t></w:r></w:hyperlink><w:r><w:t>&gt;, which you might want to solve first.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Consider a 3d grid formed by n vertices vertically down, m vertices horizontally right, l vertices horizontally front. Your starting point is at the top left front vertex. Your destination is the bottom right back vertex. (From one corner to the furthest corner) You are permitted at each vertex to choose to move down, right or back, that is in the direction towards the destination. You are not to move on what constitutes a back step like moving left, up, or front. If you hit the bottom boundary, right boundary, or back boundary, take it to be given that you move along the 2d boundary.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Ex: in a 2x2X2 grid there are 6 ways. (down, right, back), (d,b,r), (r,d,b), (r,b,d), (b,r,d), (b,d,r)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>4x3x2 has 60 ways</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>6x5x4 has 27720 ways</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This problem can be solved using dynamic programming but there are other methods too.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

This problem is inspired by <a href = "https://www.mathworks.com/matlabcentral/cody/problems/1483-number-of-paths-on-a-grid">https://www.mathworks.com/matlabcentral/cody/problems/1483-number-of-paths-on-a-grid</a>, which you might want to solve first.Consider a 3d grid formed by n vertices vertically down, m vertices horizontally right, l vertices horizontally front. Your starting point is at the top left front vertex. Your destination is the bottom right back vertex. (From one corner to the furthest corner) You are permitted at each vertex to choose to move down, right or back, that is in the direction towards the destination. You are not to move on what constitutes a back step like moving left, up, or front. If you hit the bottom boundary, right boundary, or back boundary, take it to be given that you move along the 2d boundary.Ex: in a 2x2X2 grid there are 6 ways. (down, right, back), (d,b,r), (r,d,b), (r,b,d), (b,r,d), (b,d,r)4x3x2 has 60 ways6x5x4 has 27720 waysThis problem can be solved using dynamic programming but there are other methods too.

Solve

Solution Stats

21 Solutions
15 Solvers

Last Solution submitted on Sep 30, 2020

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Asif Newaz on 8 Apr 2020

I'm getting different answers.. can u give a more clear explanation?

Problem Recent Solvers15

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44066. Number of paths on a 3d grid

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers15

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

Problem 44066. Number of paths on a 3d grid

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers15

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

Players