# P11682: Trapping the origin-first three-dimensional knight walk

- ID: `P11682`
- Reference: `trapping-the-origin-first-three-dimensional-knight-walk`
- Page: https://theoremdb.org/statements/P11682
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: f295905458d7a3b058de2e38a46a52071c41c31e
- Current Markdown: https://api.theoremdb.org/v1/statements/trapping-the-origin-first-three-dimensional-knight-walk?representation=markdown
- Record maturity: Reviewed problem

## The problem

A knight moves among unvisited points of the cubic lattice using three-dimensional moves with coordinate differences \(0,1,2\) in some order. At each step, first minimize squared distance to the origin, then minimize the number of already visited knight-neighbors, and then apply rules \(3\) through \(6\) of A343678. Is this switched-priority walk ever trapped at a point whose \(24\) knight-neighbors have all been visited?

## Status

**Resolution status:** Open.

Research work is recorded. A complete resolution has not passed review.

## Research packet

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `trapping-the-origin-first-three-dimensional-knight-walk`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.