9 . 5 I don ' t think i ' ve slept with a 10 yet . I don ' t think you ' ve slept with a 9 . 5 either . Men have been shown to consistently over rate females appearances . They are probably 6 s or high 7 s and that ' s taking you at your word . 15 And the rule of three tells us that the real number of women you e slept with is 5 . So if I had to call it I would say BB <| sep |> Would love to see more of the ass plug and play time . <| sep |> One thing you should make clearer is that by using the triangle inequality you aren ' t solving TSP , but instead metric TSP . The triangle inequality need not be true for arbitrary TSP problems . Arbitrary TSP is not constant factor approximable in a strong sense . Specifically , if you can find an algorithm that solves an arbitrary TSP within a constant factor of optimal , then you can use it to exactly find Hamiltonian cycles which is NPcomplete . One other interesting approximation algorithm for metric TSP is building a minimal spanning tree and walking around it . This won ' t be a cycle , but can be modified into a cycle and will get you within a factor of 2 of optimal . Euclidean TSP where you use the most common notion of distance is PTAS meaning you can approximate it as closely as you want in polynomial time but the polynomial get ' s scarier as you want it to be more accurate .