A Sudoku is a puzzle consisting of a three-by-three or four-by-four of spaces or numbers. The solution of a three-by-three Sudoku is to fill in the blanks with numbers 1…9 such that each three-by-three unit has only one of the numbers 1…9. Below is a worked example of a Sudoku:
4 1 7 3 6 9 8 2 5
6 3 2 1 5 8 9 4 7
9 5 8 7 2 4 3 1 6
8 2 5 4 3 7 1 6 9
7 9 1 5 8 6 4 3 2
3 4 6 9 1 2 7 5 8
2 8 9 6 4 3 5 7 1
5 7 3 2 9 1 6 8 4
1 6 4 8 7 5 2 9 3
I translated a Python program by Peter Norvig into C#. I used Norvig’s 95 “hard” to solve sudokus. It takes between thirty and fifty seconds on my home desktop to solve the 95 sudokus. Here is the tail of the run to solve the 95 sudokus. You can also solve one of the 95 sudokus by hand.
Way back in the mid-1960s there was an influential psychology book named “Games People Play” by Eric Berne, a psychiatrist, and it was based on the relatively new psychological paradigm entitled Transactional Analysis or TA for short. Transactional analysis was a replacement for Freudian analysis and human beings were represented by Parent (Super-ego), Adult (Ego), and Child (Id). The terms in parentheses are the Freudian terminology. Transactional analysis introduced the transaction which can be between Parent-Parent, Parent-Adult, Parent-Child, Adult-Child, Child-Child, Adult-Adult, and Parent-Parent. Crossed transactions such as Parent-Child, Parent-Adult, Adult-Child should probably be avoided.
Some of more popular games are “if it weren’t for you (IIWFY)” and “let you and him fight (LYAHF)”. IIWFY is a blame game. LYAHY is an ego building game for the person instigating the fight and is very popular at bars among drunks (people of diminished capacity).
The fourteen peg puzzle is a form of amusement which I have seen at my local Cracker Barrel. The puzzle involves fourteen pegs in fifteen holes in a triangular configuration. The top hole is empty. The object of the puzzle is to jump pegs over one another until only one peg is left. Jumped pegs are removed from the board.
Building the Sample
This project should build as is using Visual Studio 2008.
Description
This application was translated from a Turbo Pascal program found in Data Structure Using Turbo Pascal by Thomas M. Boger. Depth-first search with backtracking is utilized to find the solution in the allowed thirteen moves. Two stacks are used to store the moves a move stack and a reverse move stack. The translation process had to take into account a relatively strange Turbo Pascal table and an array whose base index was -1. Boger creates an array for the representation of the fourteen peg puzzle that is a right triangle for internal application operations.
These incomplete elliptic integrals are one dimensional and can be readily calculated using the Gauss-Legendre one dimensional integration technique. I use a 128 points in each integral computation. The integrals have two parameters x and k. We evaluate the F(x, k), the incomplete elliptic integral of the first kind, and E(x, k), the incomplete integral of the second kind.
Back in the 1980s a former professor of mine in mathematics at LaGrange College posed a problem to me. He handed me a deflated football and asked me to compute the volume and surface area when it was inflated. Unfortunately, I just got around to solving the problem today, Sunday, October 11, 2020. I had some help from the Casio Corporation which has a lot of free calculators on the Internet:
MeetUp.com is a website that allows a MeetUp.com Group Coordinator to hold in person (offline) and virtual (online via Zoom.com) groups. My first group is “Ballistics” which should be more exactly “Exterior Ballistics”. Below is the MeetUp.com blurb:
This group is dedicated to the study of the United States Naval Academy textbook “Exterior Ballistics, 1935” by Ernest Edward Herrmann. The contents of this book was used extensively in World War II by the United States Navy and its battleships. The group should be able to carry out ballistic calculations both classical and including drag and other trajectory corrections. Exterior ballistics is applicable to the flights of all sorts of balls including baseballs and golf balls. It is also useful for large artillery, handgun, and rifle projectile exterior ballistics. Here is an application of the methods to the Iowa class of fast battleships and their heavy armament, the 16 inch 50 caliber rifled artillery:
Back in 1982 research into electronic olfaction (electronic sense of smell, electronic nose) began. By the mid-1990s and late 1990s viable electronic nose systems were coming into existence. That means that before the 2000s we had tackled 60% of human senses via electronic means: sight, hearing and smell. That left only the senses of feel (tactile responses) and taste were yet to be conquered. The senses of smell and taste are chemically coupled. Here is a December 1995 paper on electrochemical noses their applications: https://www.researchgate.net/publication/2747174_Electronic_Noses_And_Their_Applications This maybe of interest since covid-19 may cause temporary loss of the senses of smell and taste.
Numerical Explorations 