Hi, I have a couple of basic math questions - regarding permutation and combination.
I have an 8x8 Grid, where each cel can have a binary value; 0 or 1.
If I want to find out how many variations there are, I would use the following.
8 x 8 = 64
2^64 = 18446744073709551616
First question: Did I do that correctly, to find out how many possible variations there are?
2nd question - more advanced:
Since this is a Grid, which is a square, there are four possible rotations. So after I find all the variations, I would like to remove all duplicates per rotation.
So if I take all the variations: 18446744073709551616 and say I rotate it right 90 degrees and compare the 2 result sets, then I should just be able to divide by 2 correct?
So since I have 4 rotations, then I would do: 18446744073709551616 / 4. The result of that is 4611686018427387904 unique variations.
Now once I have that done, the numbers seem simple. The big problem is knowing what pattern to keep. In other words, I believe the number is completely correct,
but with the result set of 4611686018427387904 variations, I would like to generate all the patterns that were not duplicates.
The reason for this is, that if I go through all the variations 18446744073709551616, then doing a comparison on the fly would be very time consuming. I am trying to figure
out, what the best on the fly comparison would be if I start at 0 and move all the way up to 4611686018427387904, skipping what I would discard and only saving the correct
patterns. I know there must be some simplification system, based on 4 that I can use to skip while I increment and keep only the unique patterns, but my math level is not very extensive, so I am trying to
figure out what that simplified method might be.
If you can help, thank you very much.
I have an 8x8 Grid, where each cel can have a binary value; 0 or 1.
If I want to find out how many variations there are, I would use the following.
8 x 8 = 64
2^64 = 18446744073709551616
First question: Did I do that correctly, to find out how many possible variations there are?
2nd question - more advanced:
Since this is a Grid, which is a square, there are four possible rotations. So after I find all the variations, I would like to remove all duplicates per rotation.
So if I take all the variations: 18446744073709551616 and say I rotate it right 90 degrees and compare the 2 result sets, then I should just be able to divide by 2 correct?
So since I have 4 rotations, then I would do: 18446744073709551616 / 4. The result of that is 4611686018427387904 unique variations.
Now once I have that done, the numbers seem simple. The big problem is knowing what pattern to keep. In other words, I believe the number is completely correct,
but with the result set of 4611686018427387904 variations, I would like to generate all the patterns that were not duplicates.
The reason for this is, that if I go through all the variations 18446744073709551616, then doing a comparison on the fly would be very time consuming. I am trying to figure
out, what the best on the fly comparison would be if I start at 0 and move all the way up to 4611686018427387904, skipping what I would discard and only saving the correct
patterns. I know there must be some simplification system, based on 4 that I can use to skip while I increment and keep only the unique patterns, but my math level is not very extensive, so I am trying to
figure out what that simplified method might be.
If you can help, thank you very much.