Counting Lattice Paths

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A lattice has labels A and B at opposite corners. This Demonstration determines the total number of possible paths from A to B, with moves either up or to the right. You can generate a random path from A to B or change the number of columns or rows in the grid. Check "show solution" to display an analog of a Pascal's triangle that gives the total number of possible paths from point A to all other points.

Contributed by: George Zhang (February 2017)
With additional contributions by: Deqiang Zhang
Open content licensed under CC BY-NC-SA



This was a project for Advanced Topics in Mathematics II, 2016–2017, Torrey Pines High School, San Diego, CA.


[1] M. Coffey and A. Kalish, eds., "Calendar and Solutions—December 2012," Mathematics Teacher, 106(4), 2012.

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