Question about alignment of objects Two CD’s, one is transparent and the other one is not, are partitioned into
200 equal sized circular sectors. On the first CD the sectors are coloured arbitrarily with
blue and yellow. To clarify, this means that we are given an arbitrary colouring, be it all blue, all yellow, or some irregular selection in between. This does not mean that we can arbitrarily colour the sectors.
On the second CD some 100 sectors are coloured blue and the other 100 yellow. I want to show that it is always possible to place the first CD on top of the second such that
the sectors align and at least 100 of the sectors look green.
I misinterpreted the question the first time around, and it is trivial to solve if we can arbitrarily colour the sectors of the first CD. I'm not sure how to solve the problem if the crux lies in the choice of alignment. I spent some time thinking about the problem but did not make any progress. Of course, in case the given colouring is a 'nice' one, then the proof for that case is obvious, but what about a general, irregular colouring? How does one proceed?

You can align the two CDs in 200 different ways relative to one another.
Hint 1: What's the average number of green sectors?
Hint 2:

 To sum up the total number of green sectors for all the different alignments, rather than counting the number of green sectors for each alignment, take each sector on CD1, one by one, and count the number of alignments that makes it green.

