Lattice Counting

Definition

Lattice Counting in plain English

Reach for Lattice Counting on grid paths with only right/up (or similar) moves. Clues include city blocks, lattice, only east and north, or shortest paths on a grid. Blueprint: choose positions for the required right moves among total steps, written C(total, rights). Enumerating paths on paper does not scale; the binomial counts every legal sequence once because every path is just a sequence of the same moves in different orders. If diagonal or backtracking moves appear, this tool no longer applies. Micro-example: go 3 east and 2 north on city blocks. Total steps = 5, choose 3 of them for east: C(5, 3) = 10 paths. No need to sketch every route on scratch paper.

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