Given 2 red beads, 2 blue beads, 1 yellow bead, and 1 green bead, how many different necklaces can be made?
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This is the code I have written, it is giving me an answer of 180, but the answer is supposed to be 16, what needs to be fixed?
% This script will calculate the number of possible arrangements for a
% necklace given a certain number of beads assuming circular shifts and
% flips are the same
%Create a vector with the beads where a number is assigned to each color
v=[1 1 2 2 3 4];
% 1=red
% 2=blue
% 3=yellow
% 4=green
% Determine total number of beads and all possible permutations
n=numel(v);
p=perms(v);
% Take into account colors with >1 beads
p2=unique(perms(v),'rows');
% Generate flips of all permutations
f=fliplr(p2);
% Generate circular shifts for all permutations
for i=0:n
c=circshift(p2,i);
end
% Combine the three matrices into one and remove duplicate rows
combined=[p2;f;c];
final=unique(combined,'rows');
configurations=size(final,1);
fprintf('The number of possible configurations is %d\n',configurations)
3 Comments
Walter Roberson
on 18 Oct 2019
It would make more sense to put the updated code and discussion in that other question.
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