write a matlab program that allows a user to play the 15-puzzle as well as variants of the puzzle such as the 8-puzzle, 24-puzzle, etc in matlab

Here’s an outline of the steps to create a MATLAB program to play the 15-puzzle:

1. Create a GUI (graphical user interface) with radio buttons for the different puzzle sizes (e.g. 15-puzzle, 8-puzzle, 24-puzzle, etc.).

2. When the user selects a puzzle size, generate a random initial puzzle configuration. This can be represented as a matrix, where the values correspond to the numbers on the tiles.

3. Display the initial puzzle configuration in the GUI, with each tile as a button that the user can click.

4. Implement a function that checks if a move is valid. In the 15-puzzle, for example, you can only move a tile if there is an empty space adjacent to it.

5. Implement a function that swaps the positions of two tiles in the matrix.

6. When the user clicks a tile, check if it can be moved. If so, swap its position with the empty space, and update the GUI to reflect the new puzzle configuration.

7. Periodically check if the puzzle is solved (i.e. if the tiles are in numerical order). If so, display a message that the user has won.

8. Add additional functionality as desired, such as a button to scramble the puzzle or a timer to keep track of how long it takes the user to solve the puzzle.

Here is a sample code snippet that generates a random initial puzzle configuration for a given puzzle size (in this case, 15-puzzle):

main.m
% Define the puzzle size
n = 4;

% Generate a random permutation of the numbers 1 to n^2-1
p = randperm(n^2-1);

% Add a 0 to represent the empty space
p = [p 0];

% Reshape the permutation vector into a n-by-n matrix
board = reshape(p, n, n);
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This code generates a vector of the numbers 1 to 15 in random order, adds a 0 to represent the empty space, and then reshapes the vector into a 4-by-4 matrix. The resulting matrix can be used as the initial puzzle configuration.