The Name's Donder, not Donner!

Algebra Level 4

Donder is sick of people calling him Donner all the time, so he has decided to start a tour around the world on Christmas (2015) to see how many people were calling him the wrong name.

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?

This was inspired from a discussion of the reindeer Donder's name from Day 9: The Reindeer Quiz. Thanks go to Colin Carmody for telling me this!

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