The Length of Ducci's Four-Number Game
Ron Brown, Jonathan L. Merzel · Rocky Mountain Journal of Mathematics · 2007
The length of a Ducci 4-number game, defined immediately below, is at most six if the initial vector is not cyclically monotone.If it is cyclically monotone, then the length is shown here to be, with error at most 5.4, a linear function of the logarithm of the Euclidean distance from the initial vector (normalized) to the unique normalized vector of infinite length.