Finding ways from A to B in 3d objects

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Homework Help Overview

The discussion revolves around finding the total number of shortest paths from point A to point B within a 3D grid structure, specifically focusing on x by x by x and x by y by z objects. The original poster presents a sketch of a 2 by 2 by 2 object and seeks to establish a general formula for determining the number of paths.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the constraints of movement within the 3D object, noting that movement can only occur in specific directions to maintain the shortest path. The original poster expresses uncertainty about the problem and the validity of their initial thoughts on a potential formula. Others question the assumptions made regarding the counting of paths and the interpretation of crossing multiple boxes.

Discussion Status

The conversation is ongoing, with some participants providing insights into visualizing the problem in 2D to aid understanding. However, there is no explicit consensus on the approach or formula, and the original poster's confusion indicates that further clarification is needed.

Contextual Notes

The original poster mentions difficulties in manual calculations for smaller grid sizes and the challenge of formulating a general solution. There is an indication that assumptions about movement and path counting may need to be revisited.

coldcell
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Find the total number of ways to go from A to B, if each way is the shortest route.

http://img151.imageshack.us/img151/9875/010hr.jpg

This is a rough sketch of 2 by 2 by 2 object.

I have to find the number of ways for x by x by x object and x by y by z object.

I tried doing it for 1 by 1 by 1 and 2 by 2 by 2 based on manual calcualting. However I cannot find a general formula for this.

I'm thinking x + y + z, but that's just a pure guess. I tried it on a paper, but it's too hard to show what I tried in this forum.
 
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Well, you can only go down, in, or right (depending on how you orient the figure) if you want to go the quickest way, and conversely, as long as you only go one of these three directions at each step, this is a shortest path. (Do you see why?) It might help you visualize things if you flatten the shape out and turn this into a 2D problem.
 
Last edited:
Ah yes I see it... but is it that simple?

We are assuming if we go to the right, it's 1 way. But we have in fact, crossed 2 boxes.

To be honest, I don't really understand the question myself :S
 
What? I don't follow you. There is definitely more than one way.
 

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