Originally Posted by **Guitarist**

**Always**: If I read you correctly, you have re-invented one of the most famous math puzzles of all time: it's called something like "the Konigsberg Bridge" problem. Look it up, if you want.

Anyway, assuming, as you seem to be suggesting, that no lines may intersect (cross each other), then the solution had to wait until the great Leonard Euler (say "oiler") turned his mind to it.

Supposing that "D" is the number of dots, "L" is the number of lines, and that "R" is the number of enclosed regions (i.e.those that are bounded by non-intersecting lines) he gave us the formula

D + R - L =1. For small D this is easy enough to see, for larger D it may not be

I have never seen a proof of this, but I have no doubt it would be inductive.

Nice work