Exact reachable color-state count, not an estimate.
SkimmIQ Lab · An open puzzle problem
AI can solve it.
Nobody has found the human method yet.
SkimmIQ's solver can often find a legal route back to solved in about a second. But those routes have not become a pattern language, a set of stages, or a collection of algorithms that a person can learn. That is the challenge.
Each swipe advances one 12-sticker tape by one position.
No teachable stage system or algorithm set has been found yet.
01The challenge
Find a method a human can actually use
The goal is not merely to produce one solution - the AI solver already does that. The open problem is to discover repeatable ideas: recognizable patterns, useful intermediate goals, move sequences with predictable effects, and a progression that can be taught without searching millions of states.
A genuine human method might resemble the way classic cube methods divide a solve into understandable stages. It does not have to be optimal. It has to be explainable, repeatable, and useful on puzzles a person has not seen before.
02The gap
What the AI proves - and what it doesn't
Proven
Every valid state has a route back
Exact group proofs for all six layouts show that every arrangement with the required number of stickers of each color is reachable from solved and therefore solvable. The app's solvers can usually find and replay a concrete route quickly.
Not proven
That the route teaches a person anything
Watching hundreds of machine-generated paths has not revealed a stable recipe. The paths solve individual states, but they do not yet explain which structures matter or how a person should plan.
03The state space
Why the number is exactly 1.01097 × 1038
54! / (9!)6
101,097,362,223,624,462,291,180,422,369,532,000,000
Show the full derivation
- 54 fixed positions. Master 3×3×3 has six faces with nine visible sticker positions on each face.
- Nine generators. There are three tapes on each of the X, Y, and Z axes. Each tape is a 12-position cycle; the reverse swipe is its inverse.
- The full symmetric group. An exact Schreier-Sims computation shows that these nine tape cycles generate S54, the complete set of permutations of the 54 positions. Therefore every Classic arrangement containing exactly nine stickers of each color is reachable from solved and solvable.
- Colors are indistinguishable. Classic mode has nine stickers of each of six colors. Dividing 54! by 9! for every color gives the number of distinct color arrangements.
Equivalence convention: face names, axes, and sticker positions are fixed by the game and by SQN notation, so whole-cube view rotations are not identified as the same state. Stickers of the same color are already treated as indistinguishable by the formula.
The group result was reproduced against the canonical Android movement contract and cross-checked with the independent solver-lab geometry. The computation is exact; the native replay checks validate that the proof model uses the same legal movement as the app.
04What counts as progress?
Anything repeatable, testable, and teachable
- A useful way to name recurring structures or local patterns.
- A sequence that reliably changes one feature while preserving another.
- A staged strategy that reduces the puzzle to simpler subproblems.
- A notation example, replay, counterexample, or proof that helps others test an idea.
Nobody is claiming that a human method is impossible. Nobody has found one yet. Maybe someone reading this will be the first.
05Continue exploring
Take the problem into SkimmIQ Lab
The Lab brings together the notation, browser tools, shared states and replays, and ways to contribute ideas. It is the central place for exploring the wider SkimmIQ project.