Strategy Duels
Euclid's Game
Two numbers, one rectangle. Each turn, cut away squares — subtracting a multiple of the smaller number from the larger. Reach ZERO first and you win. Hiding inside: the Euclidean algorithm, and a famous surprise — whether a position is winning is decided by the GOLDEN RATIO. Four number ranges incl. the Fibonacci marathon pairs. Solo bot ladder + live class arena.
For Educators
Built for the classroom
Division with remainder made visceral — every move IS a division step, drawn as squares cut from a rectangle. Strategy-wise, students discover forced corridors (when the ratio is under 2 there is exactly one legal move), the power of taking LESS than the maximum, and finally the theorem: a position is losing exactly when big÷small lands between 1 and φ ≈ 1.618 — the golden ratio, reached by a totally different road than geometry. The Dojo's Marathon Hunt rediscovers the Fibonacci numbers as the slowest pairs (Lamé's theorem). The boss bot plays the φ rule perfectly; beating him means using it.
Grades 5+ · Sprint ≤30 (mental math) · Classic ≤100 · Epic ≤300 (long division) · Fibonacci Duel (the marathon pairs).
Three ways to play
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Learn solo first
Four bots, all open from the start: Pebble, Chopper, Mason, Phidias. Phidias converts EVERY winnable pair — discovering what he knows is the golden-ratio theorem.
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Host an Arena
Open a room on the projector; a 4-letter code + QR + join link appear. Pick the number range, then watch live mini-rectangles shrink while the ladder climbs.
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Join on any device
Students enter the code and duel classmates. Matches rotate so everyone plays everyone — no waiting, no elimination.
Run a live class in 5 steps
- Open the Arena — pick the number range (Sprint / Classic / Epic / Fibonacci) and the move timer.
- Share the 4-letter code / QR / link; students join on any device.
- Hit "Open the Arena": best-of-2 duels on the SAME starting pair with the first cut swapped — in this game the pair decides a lot, so the swap is the fairness.
- Tap once to PREVIEW a cut (it shows the subtraction), tap again to cut. The trail of pairs builds under every board.
- The winning final cut flashes in the winner's color; the podium crowns the ladder at time.
Tip: host on a laptop or projector (the big screen shows the code, QR and leaderboard); students join on their phones or laptops.
