First problem of 2017! Ease yourself into the new year with Solve set 56 Problem 1:
The New Year gives a way to split the ups and downs of life into separate years, so that even if the last year was not so great, the next year can start fresh and we can try to get ahead. Suppose that each day is either good or bad, and we count a year as good if at least half of the days are good, and bad otherwise. Suppose that over 10 years, exactly half of the days are good and exactly half of the days are bad (but not necessarily arranged in any particular order). What is the maximum number of good years that you could possibly have?