Combinatorics and Graph Theory

1509 Submissions

[2] viXra:1509.0150 [pdf] submitted on 2015-09-17 10:04:18

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 3k 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