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
Untangle crossing lines, then work around fixed anchors and nested regions. Later puzzles require you to rearrange vertices inside the graph, not just spread them around its edge.
Connect every terminal into one network. Linked gear tiles turn their partners in the opposite direction, so every rotation can change two parts of the circuit.
Secure every zone within an energy budget. Balance cheap placements against expensive hubs, and protect fortified sectors with two or three independent neighboring beacons.
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.