Reach X: Find the Path Without Going Through Black Spaces

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Homework Help Overview

The discussion revolves around determining the number of distinct paths to a designated square marked with X on a grid, while adhering to specific movement rules and avoiding certain blocked areas. The context involves combinatorial reasoning within a grid structure, specifically related to movement constraints similar to those in checker games.

Discussion Character

  • Exploratory, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the movement options available under the given constraints, with some attempting to count the paths based on the allowed diagonal movements. Questions arise regarding the correctness of their path counts and the implications of the blocked squares.

Discussion Status

Several participants have shared their counts of the paths, with some expressing confidence in their reasoning. There appears to be a general agreement on the limited number of paths, though the discussion does not reach a definitive conclusion on the total count.

Contextual Notes

Participants are operating under the assumption that movement is restricted to diagonal forward steps on white squares only, and they are questioning the implications of the black squares on their path counts.

SeththeBaller
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How many different ways can I get to the square marked with X if I can't go through the black spaces?

http://i.imgur.com/HCSoD.png

This is the original image. Essentially, how can I get to X abiding by checker rules (a piece can only move diagonally forwards by one square at a time by only moving on the white squares. How many paths are there in total?


I counted two, because in order to get to the square directly beneath you, you must go either left then right or right then left. After that there is only one path to the x.
There is no way to go around the black squares to the left.

This is correct, right?
 
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Hi SeththeBaller! :wink:
SeththeBaller said:
… Essentially, how can I get to X abiding by checker rules (a piece can only move diagonally forwards by one square at a time by only moving on the white squares. How many paths are there in total?

HCSoD.png


I counted two, because in order to get to the square directly beneath you, you must go either left then right or right then left. After that there is only one path to the x.
There is no way to go around the black squares to the left.

This is correct, right?

Yep, looks like it! :smile:
 


Me, too. All (i.e., both) paths have to go through the white square on the right side, in the 5th row up from the lower left corner. From that square there is only one path to the X.
 


Thanks guys!
 

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