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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 prehighschool "student" (soidis)
Bob "A" r.d.acker@gmail.com