All of the fish in the pool are tagged with either tag A (10%), tag B (40%), or tag C (50%). Furthermore, we know that G is not evenly distributed among the three tags. The distribution of G is like this: 70% are A tags, 30% are B tags, and 0% are C tags.

Now, if I take a sizeable random sample from this population, the number of tags should match the ratio at which they appear in the population, so the number of that sample that is G seems like it should be:

Number sampled * ((0.1 * 0.7) + (0.4 * 0.3) + (0.5 * 0.0))

The first question is whether this is right?

The second question is making things a bit more complicated. Suppose we know that only a portion of the fish are tagged, but that ALL of the G fish are tagged and tagged at the ratio mentioned above, and that the ONLY fish sampled are tagged fish, such that they come from the tagged pool and don't include any of the untagged fish.

As I write this, it seems like the exact same equation would be the right one. In this second scenario, it seems like the untagged fish can be ignored, because the sample is taken only from the tagged fish rather than the total population of fish.

Is that right? ]]>

So the second instance would be

0000...1 <- 64 digits in binary and in hexadecimal it is 0000000000000001 <- 16 digits. basically I would like all combinations, so I would have a huge list of hexadecimal numbers from 0 to FFFFFFFFFFFFFFFF.

What would be the best way to do this. I will eventually search that list for duplicates that have different rotations or flips for example

******** *****+++

******** *****+*+

******** *****+++

******** ********

******** ********

*****+++ ********

*****+*+ ********

*****+++ ********

These correspond to hex 0000000000070507 and hex 0705070000000000, which sequentially are different but the pattern can be eliminated because of the mirror up function.

The functions I will have are mirror up down, mirror left right and rotate 90 degrees 180 degrees and 270 degrees in both directions.

I'm trying to wrap my head around how an algorithm would work with this basic set of data, so I can eliminate duplicates as necessary. After apply it to the entire range of possibilities, I want to make my function applicable to just a range.

Ok, I think I said enough. Is there a good way to do this? or is there a math example that identifies this type of problem? I thought it might be fundamental but I have not done something like this. ]]>