Before revision:  Examples where the heuristics failed had to be examined by hand . One of the digon-free intersecting arrangements of pseudocircles with n=6 is particularly interesting. It only has 8 triangles and occurs as a subarrangement of every digon-free intersecting arrangement with less than 2n-4 triangles for n=7,8,9. Hence it may be true that every digon-free intersecting arrangement of circles contains at least 2n-4 triangles .
After revision:  Examples where the heuristics failed had to be examined by hand .