# What type of puzzles are the statue puzzles in Super Lucky's Tale, and what method should be used for solving them?

This question is about a set of puzzles in the video game "Super Lucky's Tale" (as well as its Nintendo Switch remake "New Super Lucky's Tale"). They are known as statue puzzles as they involve sliding statues around.

Here is a YouTube video which shows all of the statue puzzles in the game and how to solve them.

However, I don't want someone to tell me the solution to each puzzle, I want to know what method I should use if I am trying to solve the puzzle myself. The first few puzzles in the game I solved by randomly performing actions until I solved them, but when I got to the harder ones, I found myself going around in circles. I am sure there must be some kind of methodical way to solve such puzzles.

Before anyone asks, I did post this question already over on Arqade (Gaming SE) over six months ago and no one has replied. I was hoping to get more answers on Puzzling SE.

# Basic rules and format

I will describe the puzzle conceptually so as to save people having to watch the video.

The puzzle is made up of a set of floor-tiles arranged adjacent to each other (so any tile has another tile either upward, below, to the left or to the right of it). Some tiles are marked with a "+" symbol. In the initial puzzle state, each tile either has a fox statue on it, a golem statue on it, or no statue on it. There will always be the same number of fox statues as "+" tiles.

The object of the puzzle is to get to a state where all fox statues are on "+" tiles. (The golem statues will, logically, not be on "+" tiles in this final state.)

An action in the puzzle consists of pushing a statue up, down, left or right. The statue will continue to slide across the tiles until it either runs out of tiles or hits another statue.

# Example puzzle and solution

Here I will give an example puzzle in case the above explanation was not clear. This puzzle is the one starting at around timestamp 7:50 in the above-linked video.

In this diagram,

• The letters A-E and numbers 1-3 are not part of the specification directly, they are just references to help with the explanation
• Grey squares indicate tiles
• Green circled "+" indicates a "+" tile (tiles C1, B3 and D3)
• Boxed "F" indicates the starting position of a fox statue
• Boxed "G" indicates the starting position of a golem statue

Now I will describe the solution to this particular puzzle.

Let's call the fox statue at A1 "F1", the fox statue at A3 "F2", and the fox statue at E3 "F3" to differentiate. (Please don't get confused between the fox statue references like F1 and grid references like E1!)

Goal will be to get each fox statue onto a "+" tile:

• F1 onto C1
• F2 onto D3
• F3 onto B3

Puzzle can be solved in 8 moves:

1. Push fox statue F2 to the right; it moves to position D3
2. Push golem statue to the left; it moves to position B1
3. Push golem statue down; it moves to position B3
4. Push fox statue F2 up; it moves to position D1
5. Push fox statue F1 to the right; it moves to position C1
6. Push golem statue to the left; it moves to position A3
7. Push fox statue F3 to the left; it moves to position B3
8. Push fox statue F2 down; it moves to position D3

What I am looking for is how would you solve such a puzzle methodically without having the solution, or any other puzzle of this type?

• This puzzle is a close cousin of Sokoban, which is PSPACE-Complete (i.e. very difficult). The same is probably true for this. That said, there are a few things you can do to speed up your search, like identifying the path you need a particular statue to take or checking whether the puzzle has entered an unsolvable state. Jul 19 '20 at 1:03
• I was thinking the same - this is very reminiscent of Sokoban en.wikipedia.org/wiki/Sokoban Jul 19 '20 at 11:19
• @Woofmao thanks that's useful. I think any solvable statue puzzle can be converted to a Sokoban puzzle by replacing the golem statue with a fox statue and marking its final position with +. Furthermore I think any statue puzzle solution can be converted to the equivalent Sokoban puzzle solution by converting an action to the list of Sokoban actions (noting that each Sokoban action only moves a single tile). In this way I think solving statue puzzles is at least as hard as solving Sokoban, possibly harder due to the stricter rules about actions. Jul 19 '20 at 12:09