how many combinations are in a rubix cube in matlab

To calculate the number of combinations in a Rubik's Cube, we can use combinatorics. The total number of combinations for a Rubik's Cube can be calculated by multiplying the number of possible positions for each piece. There are three types of pieces on a Rubik's Cube: corners, edges, and centers.

A Rubik's Cube has 8 corners, 12 edges, and 6 centers. Each corner can be in any of its 8 possible positions, each edge can be in any of its 12 possible positions, and each center can be in any of its 6 possible positions. Therefore, the total number of possible combinations is:

main.m
total_combinations = 8! * 3^7 * 12! * 2^11 * 6! / 2
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We divide by 2 because the centers are indistinguishable from each other.

Here's the code in MATLAB:

main.m
% Define constants
num_corners = 8;
num_edges = 12;
num_centers = 6;

% Calculate combinations
corners_combinations = factorial(num_corners) * 3^(num_corners-1);
edges_combinations = factorial(num_edges) * 2^(num_edges-1);
centers_combinations = factorial(num_centers);

total_combinations = corners_combinations * edges_combinations * centers_combinations / 2;
disp("Total number of combinations in a Rubik's Cube: " + total_combinations)
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This will output the total number of combinations in a Rubik's Cube.