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) by Charlie)

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

ALL=.5*(1+sqrt(1+8(r^2-r)))

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