Randomized array with limits

I am having a huge problem in generating a randomized array with 3 lines and for collumns that has to be of this type 2 1 3 1

3 2 1 2

1 3 2 3;

basicly the limits are in each column their has to exist at least this a number 1, 2 and 3, because it has 4 columns one of the numbers will always repeat in each line obviously, this is what i have done so far but can't seem to do better than this.

mp=[];

mp1=randperm(3)';
mp2=randperm(3)';
mp3=randperm(3)';

mp=[mp mp1 mp2 mp3]

[Walter Roberson]

If you used the same randperm for the initial mp then you would get 4 columns.

[ricardo Alcobia]

Yeah i know but it would not obey the rules, thank you anyways

Answer 1

[Rik]

A=1:3;A(4)=randi(3);
mp=A(randperm(end))

[ricardo Alcobia]

Ybut that only generates an array with 1 line, it has to have 3 lines, and even if i did that 3 times i had no guarantee that in each column there would be at least a 1, a 2 and a 3.

Thank for your help anyways!

[Rik]

Do you also have a rule for each row?

Answer 2

[Image Analyst]

Try this:

% Initialize.
rows = 3;
columns = 4;
% Each row of A starts out like [1, 2, 3, rowNumber] to follow the poster's example/directions.
% So first row will have 2 1s, second row will have 2 2s, and third row will have 2 3s.
A= [repmat(1:columns-1, [rows, 1]), (1:rows)']
mp = A;
% Go down each row, scrambling the columns
for row = 1 : size(A, 1)
	order = randperm(size(A, 2));
	mp(row, :) = A(row, order);
end
mp

You'll see

A =

1 2 3 1

1 2 3 2

1 2 3 3

mp =

1 2 3 1

2 3 1 2

1 3 3 2

as required.

[ricardo Alcobia]

That does not obey to the fact that every column has to have at least one of each number, thanks for your help!

Btw I already found a way to do this!

a=0;

while a<8

MP1=randperm(3);

MP2=randperm(3);

MP3=randperm(3);

MP4=randperm(3);

MP=[MP1;MP2;MP3;MP4]';

mp11=1;

mp22=1;

mp33=1;

for j=1:4

mp1=MP(1,j);

mp11=mp11*mp1;

mp2=MP(2,j);

mp22=mp22*mp2;

mp3=MP(3,j);

mp33=mp33*mp3;

end

b=prod(MP,'all');

if mp11==18 | mp11==12 | mp11==6

ab=2;

else

ab=0;

end

if mp22==18 | mp22==12 | mp22==6

aa=2;

else

aa=0;

end

if mp33==18 | mp33==12 | mp33==6

aaa=2;

else

aaa=0;

end

if b==1296

aaaa=2;

else

aaaa=0;

end

a=aa+aaa+aaaa+ab;

end

MP

[Image Analyst]

I guess I misinterpreted what you said and your example. Try this code (much shorter and simpler than yours):

% Initialize.
rows = 3;
columns = 4;
% Each column of A starts out like [1; 2; 3].  Each row will be the row number.
% then we'll scramble the order of the rows, column-by-column.
mp = [repmat((1:rows)', [1, columns])]
% Go across each column, scrambling the rows in each column.
for col = 1 : columns
	order = randperm(rows);
	mp(:, col) = mp(order, col);
end
mp

You'll get, for example:

mp =

1 1 2 2

3 3 1 3

2 2 3 1

Looks like you maybe want a "Latin Rectangle". Have you ever heard of that?

https://en.wikipedia.org/wiki/Latin_rectangle

[ricardo Alcobia]

yeah that is it thank you very much