How many total gifts in the twelve days of christmas if we extend 12 to any number? <p>I got this question today in an interview: write a function to calculate the total number of gifts received for any day in the 12 days of christmas song. I wrote a simple function using a for() loop in c#'ish code that worked. Then the interviewer asked me to extend it to any number of days. The conversation then turned to how to optimize the loop. Apparently there's a cool math trick that will do this within the limits of whatever your integer is. Anyone know what it is and what it's called? Any language is ok and a reference to the algorithm would be fabuloso.</p> <p>Answers that use recursion are NOT what I'm looking for.</p> <p>EDIT: Answer for day 2 is 4 gifts total, not 3 since I will have 2 Trees (1 from today, 1 from yesterday) and 2 partridges. On day 12 I'll have received a total of 364. I want the formula that lets me input 12 and get 364.</p>