how to generate all possible combinations of a 14x10 matrix containing only 1's and 0's

Question

I\'m working on a problem and one solution would require an input of every 14x10 matrix that is possible to be made up of 1\'s and 0\'s... how can I generate these so that I can

Answer 1

This is absolutely impossible! The number of possible matrices is 2¹⁴⁰, which is around 1.4e42. However, consider the following...

• If you were to generate two 14-by-10 matrices at random, the odds that they would be the same are 1 in 1.4e42.
• If you were to generate 1 billion unique 14-by-10 matrices, then the odds that the next one you generate would be the same as one of those would still be exceedingly slim: 1 in 1.4e33.
• The default random number stream in MATLAB uses a Mersenne twister algorithm that has a period of 2¹⁹⁹³⁶-1. Therefore, the random number generator shouldn't start repeating itself any time this eon.

Your approach should be thus:

• Find a computer no one ever wants to use again.
• Give it as much storage space as possible to save your results.
• Install MATLAB on it and fire it up.

• Start computing matrices at random like so:

  while true
    newMatrix = randi([0 1],14,10);
    %# Process the matrix and output your results to disk
  end
  

• Walk away

Since there are so many combinations, you don't have to compare newMatrix with any of the previous matrices since the length of time before a repeat is likely to occur is astronomically large. Your processing is more likely to stop due to other reasons first, such as (in order of likely occurrence):

• You run out of disk space to store your results.
• There's a power outage.
• Your computer suffers a fatal hardware failure.
• You pass away.
• The Earth passes away.
• The Universe dies a slow heat death.

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NOTE: Although I injected some humor into the above answer, I think I have illustrated one useful alternative. If you simply want to sample a small subset of the possible combinations (where even 1 billion could be considered "small" due to the sheer number of combinations) then you don't have to go through the extra time- and memory-consuming steps of saving all of the matrices you've already processed and comparing new ones to it to make sure you aren't repeating matrices. Since the odds of repeating a combination are so low, you could safely do this:

for iLoop = 1:whateverBigNumberYouWant
  newMatrix = randi([0 1],14,10);  %# Generate a new matrix
  %# Process the matrix and save your results
end