Question 10
During a $40$-day period, Andy saved money every day except on $4$ skipped days. On day $n$, where $1\le n\le40$, if he did not skip that day, he saved $n$ dollars. Otherwise, he saved nothing. The four skipped days formed two disjoint pairs of consecutive days, with at least one day between the two pairs. Andy never skipped more than two consecutive days. If Andy's total savings over the forty days were $766$ dollars, how many possible patterns of skipped days are there?