The Name's Donder, not Donner!Algebra Level 4
He will spend \(n\) days in 1 place, then \(n-1\) days in 2 places, then \(n-2\) days in 3 places, \(\dots\), 2 days in \(n-1\) places then 1 day in \(n\) places. Assume that his travelling does not take up time (as he factors that into his stay at each place). (\(n\) is a positive integer.)
His tour can be at most 365 days long as he must get back to Santa on Christmas Eve. (Yes, 2016 is a leap year)
What is the maximum length of his tour in days?