## The n X n X n Dots Problem: An Improved “Outside the Box” Upper Bound

**Authors:** Marco Ripà, Valerio Bencini

In this paper we describe two new patterns, in order to improve the upper bound for the Ripà’s n X n X n points problem, saving a few lines for many values of n. The new upper bound, for any n≥6, becomes h_u(n)=int((3/2*n^2)+int(n/4)-int((n-1)/4)+int((n+1)/4)-int((n+2)/4)+n-2, where int(x)≔floor(x).

**Comments:** 14 Pages.

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### Submission history

[v1] 2018-07-23 09:53:39

[v2] 2018-07-25 16:31:37

**Unique-IP document downloads:** 65 times

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