# 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?

×