Three pure algorithmic puzzles built from first mathematical principles. No trackers, no paywalls, zero external dependencies. Pure client-side Canvas and Web Audio.
Play seamlessly inside the portal or launch full-window standalone
Unravel knot topologies by dragging vertices until zero line segments intersect. Grounded in Fáry's theorem and planar graph straight-line embeddings.
Rotate circuit tiles to connect every terminal into a unified, cycle-free spanning tree network. Features dynamic grid scaling from 3×3 up to colossal 16×16 grids.
Position a limited sentinel garrison across complex node topologies to satisfy multi-link defense requirements. Features path projections and shield bracket harmonics.
Every mechanic directly implements a fundamental theorem in discrete mathematics
V - E + F = 2
A graph is planar if and only if it can be drawn in the Euclidean plane without any edges crossing. By Kuratowski’s Theorem, a finite graph is planar if and only if it does not contain a subgraph homeomorphic to \(K_5\) (complete 5-graph) or \(K_{3,3}\) (utility graph). UntangleLeft generates guaranteed-planar embeddings and scrambles their spatial coordinates, challenging players to recover straight-line embeddings assured by Fáry's Theorem.
au(G) = rac{1}{|V|} \lambda_1 \lambda_2 \dots \lambda_{|V|-1}
A spanning tree of a connected graph is a cycle-free subgraph that visits every vertex. Kirchhoff's Matrix Tree Theorem expresses the number of spanning trees via Laplacian eigenvalues. FluxLeft utilizes Wilson’s algorithm with loop-erased random walks to guarantee uniform distribution over the set of spanning trees across grid lattices up to 16×16 (\(256\) vertices, \(480\) candidate edges).
\min |D| \quad ext{s.t.} \quad orall v \in V, \; |N[v] \cap D| \ge k(v)
The Minimum Dominating Set problem is one of Karp's 21 NP-complete problems. SentinelLeft extends this into Generalized \(k\)-Domination combined with Hashi (Bridges) multi-degree constraints: target nodes mandate direct, concurrent coverage from multiple adjacent sentinels. Calculating exact minimum sentinel garrisons transforms defense positioning into combinatorial tactical optimization.
Software should respect its players. Modern gaming is inundated with predatory microtransactions, behavioral telemetry, data harvesting, and forced account lock-ins.
Left Gaming is committed to Strong Copyleft (GNU General Public License v3.0+). Every puzzle here is written in clean, zero-dependency modern JavaScript and HTML5 Canvas. No cookies, no trackers, no paywalls, and no external CDNs required.
You have the absolute right to run, study, modify, and share this software. The code belongs to everyone, in perpetuity.