Tip, stand, roll
Standing on one tile, the block can tip flat. Lying across two tiles, it can stand up or roll sideways. It never slides.
A one-domino puzzle
Tip. Stand.
Roll. Find
the hole.
A 1 × 1 × 2 block on a finite floor. One hole. No timer. Every move has to land on solid ground.
- Grid
- 13 × 9
- Hole
- 1
- Layouts
- ∞
Preview · 7 × 5
01 / Play
Endless, and offline.
Every layout is generated from a random walk. The floor is carved, the final standing tile becomes the hole, and you get one block and four directions. Levels unlock in order; completed levels stay replayable.
02 / The rules
Three things to remember.
The block is rigid. The floor is the only support. The hole is the only target.
Floor is support
Every tile under the block must be floor. A lying block gets one exception: one end may hang over the hole, if the other end is floor.
Stand on the hole
Only standing on the hole wins. Lying across it is a safe rest, never a win. A fall returns the block to its last safe position.
03 / Research
Why modulo 3?
Each tile has a phase: two remainders, (x mod 3, y mod 3). Tips preserve the phase. Side-rolls move one coordinate by one and need a 2 × 2 patch. That gives a quick impossibility test, a corridor formula, and a lower bound on rolls.
The short version
- Phase two remainders
- Tip phase stays
- Roll one step sideways
- Best shortest BFS path
Includes the formal rules, a Lean 4 specification, and Python and JavaScript solvers.