Strategy Duels
Factor Chains
The numbers 1–100 are the board. Take turns claiming numbers in ONE shared chain — every claim must be a factor or multiple of the claim before it. Run out of moves and you lose. Primes are power moves, 1 is a trap, and the whole game secretly runs on a pairing theorem deep enough to power a PERFECT boss bot. Three board sizes + two opening rules. Solo bot ladder + live class arena.
For Educators
Built for the classroom
Factors, multiples, and primes as STRATEGY — every claim is a divisibility check the student wants to make. Players discover the chain-killers (primes over half the board touch only 1), the role of 1 as the universal hub, and real opening theory: on the 1–40 board exactly TWO openings win with perfect play (22 and 26 — doubled primes!). The boss, the Matchmaker, plays a maximum-matching strategy that is mathematically PERFECT — beating her requires genuine mastery, and doing it unseals the Dojo's theorem page (vertex geography, the pairing rule, computed verdicts for every board). The Dojo's Partners lab plants the pairing idea by hand.
Grades 4+ · Sprout 1–20 (mental math) · Grove 1–40 (sharp openings) · Forest 1–100 (the classic) · Classic rule (first claim even) or 🌶️ Wild (find out why the rule exists).
Three ways to play
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Learn solo first
Four bots, all open from the start: Inchworm, Hopper, Weaver, and the Matchmaker — who answers every claim with its pre-paired partner. Perfectly.
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Host an Arena
Open a room on the projector; a 4-letter code + QR + join link appear. Pick the board + opening rule, then watch live mini-grids fill 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 board (Sprout / Grove / Forest) and the opening rule (classic even-first, or Wild for a lesson in why rules exist).
- Share the 4-letter code / QR / link; students join on any device.
- Hit "Open the Arena": best-of-2 duels on the same board with the first claim swapped — the opening is half the battle, so the swap is the fairness.
- Tap once to CHECK the arithmetic (does it divide?), tap again to claim. The chain strip tells the story above every grid.
- When a student has no factor or multiple left, the chain dies in their color — ask the room: which claim actually killed it? Podium 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.
