Question 9
A quadruple $(a,b,c,d)$ of positive integers is skewed if the median and mode of $a,b,c,d$ are equal, but strictly greater than the mean of $a,b,c,d$. How many skewed $(a,b,c,d)$ of positive integers are there that satisfy $a\le b\le c\le d$ and $a+b+c+d=40$?