Tiltmaze

Tiltmaze is a series of puzzles. They are much better played interactively, but because I’m too lazy to make an applet for it, it’s going to be simply an image. You have to imagine yourself. They are also in some sense optimization.

The objective is to bring all the “balls” to the “goals”. However, you won’t be controlling them directly. You will tilt the entire grid to one of the four cardinal directions every move; most objects move in that direction until they hit something and hence cannot move any more.

Attributes (all of these might be overridden if specified such)
Slides / Moves / Doesn’t move: Every tilt, an object that “slides” will move in said direction until bumping to another object; an object that “moves” will move a specified number of squares in said direction unless it will bump in which it will move the most number of squares without bumping; an object that “doesn’t move”…doesn’t move, it stays perfectly still.
Solid / Non-solid: A “solid” object occupies space, and so by extension of Pauli exclusion principle no two solid objects can phase through each other. This means two solid objects can “bump”. For example, a ball against a wall will stop at the cell right before phasing through the wall, and a ball against another (that is stationary) will stop right before going to occupy the same cell as the latter ball. No such thing happens with “non-solid” objects against anything.
Cell / Border: A “cell” object occupies a single cell. A “border” object occupies the border (unit segment) between two cells.

Objects
Fundamental objects
– Ball (green solid circle): An object that you should guide to the goal (see below). Cell; slides; solid.
– Goal (thin blue circle): The destination where a ball should be guided (see above); ball must be stationary in order to count. Cell; doesn’t move; non-solid.

Blockers
– Wall (thin black border): An impenetrable wall; causes most objects to bump to them. Border; doesn’t move; solid.
– Cliff (black border with arrows): A one-sided wall. Objects coming from the…uh…”open” side phases through the cliff (jumps down), but objects coming from the “closed” side bumps to the cliff like it’s a wall. Border; doesn’t move; somewhat solid (read ←).
– Box (olive solid circle): A regular object, impenetrable. Cell; slides; solid.

Antagonists
– Enemy (red solid circle): Bad thing, don’t touch. When a ball hit an enemy (or an enemy hit a ball), the ball is destroyed (and you lose). A ball and an enemy that are simply occupying adjacent cells don’t cause you to lose, but if one of them move toward each other (and there is no wall), it will still cause a hit and hence a loss. Acts as a regular object otherwise. Cell; slides; solid.

Example
Mechanics

Example grid

Example grid

The above is an example grid. You may use any number of moves to complete the objective, although it’s a neat secondary objective if you can match (or beat) my solution 🙂

So, here’s the above grid after the move ↑ (up):

After move ↑

After move ↑

The fastest solution to this puzzle can be easily proven to be 4 moves: ↑←↓→. (There also exists a solution with 7 moves →↑←↑←↓→, and you can easily extend any solution by including useless moves, such as inserting a → after the ↑ in the best solution.) Note that the 2-move sequence →↑ is not a solution, since the ball must stop right at the goal (and not simply passing it; in other words, winning condition is only checked between moves).

Multiple objects

Example grid

Example grid

Everything moves together, since you tilt the whole grid. So, after a move ↑, the grid looks as follows:

After move ↑

After move ↑

Also, when a solid cell object bumps to another, the solid cell object stops at the cell right before the latter. So, if we move →, the grid looks as follows:

After moves ↑→

After moves ↑→

The fastest solution to this puzzle is ↑←↑→↑, which utilizes a box at R1C4 so the ball, moving ↑, can stop at R2C4 and completing the puzzle.

Puzzles
Tutorial Pack
Tiltmaze 1: The Plains
Tiltmaze 2: Divided By Two
Tiltmaze 3: Sacrifices

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