An examination of some permutations of ratios.

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Excel format

Numbers format

Premise for understanding:

You meet two girls of the Johnson family, both of them have blue eyes. What is the ratio of blue eyed girls to non-blue eyed girls that will allow the percent chances of meeting two blue eyed girls to a pair who do not have blue eyes 50% - 50%.

This means your objective is to have the same amount of combinations of blue eyed girls (2 at a time) as the amount of combinations of two non-blue eyes AND 1 non-blue and 1 blue. 

  Blue       |      non-blue
A,B,C	           |          D 
AB, AC, B,C       |    DA, DB, DC 
    3	          |          3 

   Or   50% to 50%

Is this really the only combination that will work? Seems unlikely, that is why I created this table. However creating it has only engendered more questions than I care to answer, yet an irresistible urge is guiding my persistence.

For some reason I believe this patter of numbers, or possibly many patters of numbers may lead to mathematical proof of my theories of infinity. How numbers the three infinities can exist in seemingly normal problems. Whether or not my more abstract idea of a fourth infinity involving the value of a number being changed can be proven mathematically is yet to be answered, however I have recently theorized that this idea may simply be a subset of my third proposition: infinite combinations of each infinite permutations of each infinite objects. Yet another idea of infinity could be an attribute of a number not yet accounted for in the above statements; the idea that each numbers value is affected by the amount of times it is repeated. For instance if i type 1 now, it has a different value than when I type it now 1. I’m naming this idea the “precedent effect.”