Shadow Garden

For Educators

Built for the classroom

That light travels in straight lines — so a shadow falls exactly OPPOSITE the sun and stretches farther when the sun is low — turned into a coverage puzzle. Each round gives a top-down garden of scattered plants (and rocks that block shadows); students place a few parasols on open ground so their straight shadows, cast away from the sun, cool the most plants. The catch is that no single parasol can shade them all: the shadows have to work TOGETHER, which makes it a genuine set-cover / facility-location problem, not a calculation. The reveal drops every garden's shadows at once on the projector, so students SEE which placements cooperated. The deep idea, in the gated theorem: the straight ray makes shadow length = height ÷ tan(the sun's altitude) — the geometry of a sundial, and of how Eratosthenes measured the Earth from two shadows in 240 BC — and covering everything with as few parasols as possible is the same math that sites solar panels, cell towers, and security cameras. The deeper twist (2026 redesign): with a single sun every shadow is one straight stripe and the stripes nest — a "laminar" cover on which the greedy "cool-the-most-now" move is always perfect, so single-sun gardens never actually require reasoning (greedy == optimum on 2,000/2,000 random boards). So each parasol now casts TWO shadows — morning + noon, an L-shape — which lets shadows cross instead of nest, breaking laminarity; plus 🌳 trees that throw their own free shade and block rays. Our check (101 green) proves the shadow falls 180° from each sun, is cut short by rocks and trees, that the exact coverage optimum matches brute force, and — the headline — that on EVERY served board the greedy move PROVABLY falls short of the optimum by the tier's gap (so the locally-best parasol is the wrong move), the exact search stays tractable, and a deterministic, pre-baked board bank scores exactly what each device renders.

🎓 Grades 3+ · a top-down garden from 5×5 up to 8×11 of plants 🌱, open ground, and rocks 🪨 · solo is a head-to-head run vs four rivals — out-shade 🌞 The Gardener on Tough/Brutal for the Gardener's License · live rooms shade the same garden secretly, then every garden's shadows fall on the projector at the reveal.