Tortoise and hare can actually tell you which node the cycle starts on.

  1 -> 2 -> 3 -> 4 -> 5 -> 6
            ^              |
            |______________|

  Step:       0 1 2 3 4
  Tortoise:   1 2 3 4 5 
  Hare:       1 3 5 3 5 <- pointers reference same node, cycle exists

Then create another tortoise pointer at the head, iterate until both tortoises point to the same node.

  Step:       0 1 2
  Tortoise:   5 6 3
  Tortoise2:  1 2 3 <-cycle starts at 3