## 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.

**Download:** **PDF**

### Submission history

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

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

**Unique-IP document downloads:** 98 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*