Brain Teaser Answer

What is the average percentage of the yellow section that is backed up in each day
of the four day cycle (i.e., assuming the 15% change is uniformly distributed)?

Day 1 100%, since this is its partial full backup.
Day 2 15%, since this is the daily change rate.
Day 3 27.75%, computed as 30% - (15% of 15%) = 30% - 2.25%.
The first term is the maximum incremental size (if the overlap was 0): 2 * 15%. The second term is the overlap: the part of the 15% backed up on day 2 that changed again on day 3.
Day 4 45% - (15% of 27.75%) = 45% - 4.16% = 40.84%