If you take two balls randomly out of a jar of colored balls, there is a 50% chance that the balls will both be red.
What is the total percentage of red balls in the jar?
(In reply to Another solution (re: a mathematecally more rigorous solution)
I saw this puzzle recently and after solving it at the d2 level went thru solvers posts, since I got two solutions, and the official solution cited only one.
My approach was: there are r*(r-1)/2 possibilities of choosing 2 red and ALL*(ALL-1)/2 possibilities of choosing ANY 2 marbles.
Comparing twice the former with the latter boils down to
A^2-A+2*r-r^2=0, resolved as
3,4 and 15,21 fit getting an integer pair and reaching
a conclusion that there is more than one solution.- actually infinity.
I was relieved to see your post and decided to chip in my humble contribution.
The original puzzle would be politically correct by adding a constraint like "out of a jar containing no more than 30 colored balls"... etc