Question: Must every year have at least one Friday which is on the 13th? By listing out all the dates, I found that for any year, day 1st-7th must appear at least once for the the first Friday of the months. Hence, there must be at least a month which the first Friday is on the 6th. Thus, I deduce that every year must have at least one Friday which is on the 13th. But how do I prove it mathematically? Does the dates form sequence? Is calculus needed for this question?