my dad (actuary) and I (journeyman maths student) looked at this in 1950s.... we thought the rule was:
even disks left
odd disks right
additional "modulus arithmetic" tuition about going around to the other side
seemed cool and simple..... graph theory is also cool but harder for pre-highschool "student" (soi-dis)

Bob "A" r.d.acker@gmail.com