|Spoiler Inside: Solution to Puzzle||SelectShow>|
This is a sucker problem. Most of the data is irrelevant. When solving a problem, first determine which data is relevant to the solution.
1) Fluffy might take out one feather duster in a day, never more, so it will take at least four days to take out the four feather dusters.
2) Odd-numbered days are usually followed by even-numbered days so usually, there is only one odd-numbered day “in a row”. The exception is at the end of a month with an odd number of days (e.g. January). In that case, the 31st (or 29th) of one month is followed by the first of the next month so two in a row. There is no way to have three in a row though so the probability is 0.