counting-principles

Two side-by-side animated panels show how counting works for (1) disjoint alternatives using the addition rule |A ∪ B| = |A| + |B| by revealing elements in sets A and B, and (2) sequential independent choices using the product rule |A × B| = |A| * |B| by filling a Cartesian-product grid of ordered pairs.

canvasclick to interact

t=0s

practical uses

01.Counting outcomes with either/or choices (e.g., choose soup OR salad options)
02.Counting multi-step configurations (e.g., password format: 3 digits then 2 letters)
03.Estimating combinations in UI flows (e.g., A/B test variants across multiple independent toggles)

technical notes

Uses time-based stepping to reveal elements (discrete counting) and a scanning fill to build the Cartesian product grid. Blocky look comes from snapped coordinates and square “dot” markers; colors follow GREEN/GREEN_DIM on black with a subtle grid. Mode alternates every 4s to focus attention on one rule at a time.

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