We should add a couple twists to this puzzle:
1) How many different unique solutions exist?
2) Can you determine a set of positive integer numbers that makes a unique solution? If not, what is the minimum sum required to form a unique solutions (i.e. all add to 50 instead of 25).
I'm not sure I understand what you are mean - the question is about circles, not hexagons. There is no possible way to fill up all white space. I believe there will be conditions where it is optimum not to put the circles into the recesses. You are limited to 1 circle every two recesses doing this - try it out. You will see the effect as the size of the smaller circles decrease.
A note about the 'least number of circles': I assumed that he just made a typo - it would be fairly obvious that 1 is the least number of circles as long as it is smaller.