Let us call a sum of integers cool if the first and last terms are 1 and each term differs from its neighbours by at most 1. For example, the sum 1+2+3+4+3+2+3+3+3+2+3+3+2+1 is cool. How many terms does it take to write 2008 as a cool sum if we use no more terms than necessary?
I found there are 89 terms needed. Maybe there is another that lesser?