KöMaL 2010 K247

During the first three years of her life, Sleeping Beauty slept an average of 14 hours a day. Then, until she was 16 years old she slept 8 hours a day, and then from her 16th birthday onwards, when she wounded her finger with the reel, she slept 24 hours a day for 100 years. A filbert mouse hibernates for 5 months of the year (from 1 November to 31 March), and in the rest of the year it spends a daily average of 8 hours awake (during the nighttime hours). After how many years of sleep should the prince have woken up Sleeping Beauty so that her daily average of sleep from her birth to her waking up equals that of a filbert mouse? (For simplicity, ignore leap years, that is, assume that February is always 28 days long.)