I got hold of the super awesome book I read 6 years back: "A Path to Combinatorics for Undergraduates: Counting Strategies". A must have for any math/olympiad enthusiast (Flipkart link to Imported Edition and Indian Edition) - Example 5.8 - USAMO 1990
Let n be a positive integer. Find the number of positive integers whose base n representation consists of distinct digits with the property that except for the leftmost digit, every digit differs by +1 or -1 from some digit further to the left.
No correct solution provided. Solution posted by me in comments!