Question 192
The Dingoberry Farm is a $10$ mile by $10$ mile square, broken up into $1$ mile by $1$ mile patches. Each patch is farmed either by Farmer Keith or by Farmer Ann. Whenever Ann farms a patch, she also farms all the patches due west of it and all the patches due south of it. Ann puts up a scarecrow on each of her patches that is adjacent to exactly two of Keith's patches (and nowhere else). If Ann farms a total of $30$ patches, what is the largest number of scarecrows she could put up?