# Combinatorics and Graph Theory

## 1509 Submissions

[2] **viXra:1509.0150 [pdf]**
*replaced on 2018-07-22 18:49:24*

### Ripà’s Conjectures on the K-Dimensions 3 X 3 X … X 3 Dots Problem

**Authors:** Marco Ripà

**Comments:** 5 Pages.

The classic thinking problem, the “Nine Dots Puzzle”, is widely used in courses on creativity and appears in a lot of games magazines. Here are two mutually exclusive conjectures about the generic solution of the problem of the 3^k dots spread to 3 X 3 X … X 3 points, in a k-dimensional space.

**Category:** Combinatorics and Graph Theory

[1] **viXra:1509.0140 [pdf]**
*replaced on 2016-12-01 05:58:16*

### A Computer Program to Solve Water Jug Pouring Puzzles.

**Authors:** Richard J. Mathar

**Comments:** 33 Pages. Added more references and more explicit solutions in Version 2.

We provide a C++ program which searches for the smallest number of pouring steps
that convert a set of jugs with fixed (integer) capacities and some initial known (integer)
water contents
into another state with some other prescribed water contents. Each step
requires to pour one jug into another
without spilling
until either the source jug is empty or the
drain jug is full-because the model assumes the jugs have irregular shape and no
further marks.
The program simply
places the initial jug configuration at the root of the tree
of state diagrams and deploys the branches (avoiding loops) recursively by
generating all possible states from known states in one pouring step.

**Category:** Combinatorics and Graph Theory