If you have two buckets, one with red paint and the other with blue paint, and you take one cup from the blue bucket and poor it into the red bucket. Then you take one cup from the red bucket and poor it into the blue bucket. Which bucket has the highest ratio between red and blue? Prove it mathematically.
Kind of a trick question. What if the buckets only contained 1.1 cups of paint?
Since the paint is conserved we can say that if after the pouring back and fourth over N cycles (here N=1) an ammount a of paint is transfered from the red to the blue bucket then we can see that the relative ratios are:
[(X-A) Red / A Blue] in the red bucket and [A/(X-A)] in the blue bucket.
As logn as (X-A) is greater than A we have proven the above statement.