Another way of thinking about it: You have values of 13 down to 1, but
the outer values are fixed, so 11 places have to share the values 12
down to 2, i.e. 77 points. However, the lowest value for each member of
this group of 11 is 1 (they can't be lower than the lowest!), so you
only have 66 points to share between them, and the "share" for each has
to be added to 1.

More or less the same conclusion you arrived at.

Pete