A Musing on the Sudoku Numerical Puzzle

Sudoku apparently is the hottest puzzle game in years. Resembling the grid of a crossword, it's a deceptively simple idea that's both fun and frustrating to solve.

The idea is that you start with a 9x9 grid, subdivided into 9 3x3 grids, with a few seemingly random numbers from 1 to 9 shown. The trick is that within any 3x3 grid, you may only fill in the remaining cells with the digits 1-9, never repeating a digit. What's more, the same digit may not appear more than once in any given row or column in the full 9x9 grid. Therein lies the fun of this puzzle.

The first time I tried Sudoku, I found myself immediately addicted. But then again, I'm a math geek with an interest in game theory. Years ago in high school, I first tried solving the "8 Queens Problem", which is in some ways similar to the problem of creating a Sudoku grid. (Solving a Sudoku puzzle uses different techniques.)

The good thing is that thousands of non-math geeks love this puzzle. It's really a lot of fun, espcially if you like puzzles and board games. I've come across a few websites, but the best free Sudoku game I've come across to date is over at Life magazine's site. However, you may need the Macromedia Flash/Shockwave plugin for your browser. (If you do, the page will tell you so, and provide a link.)

I've managed to bring my initial times of about 56 minutes down 13-25 minutes regularly. But don't expect to play and watch TV at the same time, or you'll end up taking an hour per puzzle like I was.

Keep an eye out here or on the new website, http://www.getyergameon.com/, for some pointers in solving Sudoku puzzles, both on paper and online.

(c) Copyright: 2006-present, Raj Kumar Dash, http://www.getyergameon.com/

Technorati Tags: getyergameon, sudoku, game grids, numeric puzzles

The Eight Queens Problem - Game Theory

I've always been fascinated by chess, but could never find regular challengers. So I often turned to computers and researching the mathematical aspects of chess. Many years ago, when I was in high school, and computers were about the size of a car, I attempted to solve the Eight Queens problem using what is known in computer lingo as "brute force". That is, by trying every possible combination.

If you're not familiar with the Eight Queens problem, it asks the question, "Can 8 queens be placed on a standard chessboard in such a way that none of the queens can capture one of the other queens?"

I won't get deep into a mathematical discussion of this problem, but suffice it to say that the brute force method is as naive as the mythical king who agreed to pay his minister in grains of rice - especially since the computer I was using was a huge old IBM beast about the size of a large closet.

It wasn't bad enough that I started a computer "job" attempting to try all possible combinations for placing the 8 queens on a standard 64-square chess board. I also decided to print out diagnostics for EACH attempt. And this on a giant IBM feed printer, where the paper hooked into metal pin rollers. (Laser printers didn't even exist back then.)

I was waiting in the print room for my printout, when a certain loud Italian professor in his unusual accent - that I could never figure out - came roaring into the basement room, presumably having run down from the 3rd floor. (Our high school had an agreement with the local college's computer department.)

"Who the hell crashed the computer?!!". That's all I remember. He was fuming, but upon seeing me, whom he'd known since I was a kid, he calmed down., never suspecting it was me, even with the pages of diagnostics spewing out of the printer.

My attempt to solve the Eight Queens problem was written with an erroneous infinite loop, and brought the department computer down, as well as probably wasting loads of paper. I didn't stick around. I snuck off out of there before the professor figured out it was me. Even a couple of years later, in college, when I had him for a computer science professor, he still hadn't figure out it was me.

To this day, I've never revisited the Eight Queens problem. Not even to read up on it, until now. The University of Utah website has a page discussing the "12 essentially distinct solutions" to the 8 Queens problem, as well as a graphic showing the 12 configurations. Aaron Davidson has an easy to use 8 Queens Java applet that will display solutions.

(c) Copyright: 2006-present, Raj Kumar Dash, http://www.getyergameon.com/

Technorati Tags: getyergameon, get yer game on, chess, game theory

The Origins of Chess And Other Tidbits

Everyone has their own version of how they think the game of chess started. The version I heard from my father, now a retired math professor, over 30 years ago goes something like this...

Once upon a time, there was a very naive king in India. His very loyal minister tried in vain to teach the young king the protocols of being a nation's leader, and the subtleties of war. The minister failed at every attempt that he could.think of.

Finally, he invented the game of chess, as a tool for teaching the king about war, strategy, and consequences of actions. Nevertheless, the king still didn't get it, naive as ever.

In frustration, the minister challenged the king to a bet. "Your highness, if I win the bet, then you must give me a certain amount of rice. The amount will be determined by placing one grain of rice on the first square of the chess board, then doubling that number on each successive square, until the 64th square is reached." (My apologies, but I can't remember the nature of the actual bet.)

The king thought for a second, then said, "Sure. No problem."

The minister threw his hands up in the air, then explained to the king that by the time the amount of rice grains for the 64th square was calculated, there wouldn't be enough rice left in the world.

Apparently, the king caught on to this concept, and somehow, this helped him to understand chess better, and thus the protocols of war.

(c) Copyright: 2006-present, Raj Kumar Dash, http://www.getyergameon.com/

Technorati Tags: getyergameon, get yer game on, chess, game theory

Does Chess Make You Smarter?

Gina Damron writes in the Oakland County Free Press (links below) about a group of 3rd graders that have chess-playing as part of their school curriculum. According to the article, and testimonials from the participating teacher and 9-year olds, learning and playing chess has made them better at not just math, but has also improved their attention spans.

"Chess is making me better at math," the 9-year-old said. "It just kind of makes me think more."

I would hazard a guess that playing chess also develops IQ and builds a mind that can strategize. To those of us that play chess, this should come as a no surprise. (Have you ever heard of a stupid chess player?)

I know that as a former hyperactive kid, chess gave me some discipline, even when my brother and I played "atomic speed chess" as a kids, with the intent of capturing as many opposing pieces as fast as possible, and with the minimum of strategy.

Being forced to think several moves ahead in your mind builds the ability to consider not only your options, but the consequences of your actions. In other words, chess players develop analytic minds. That this results in a better attention span is a bonus.

All this warrants the question: does playing chess require an initially bright mind, or can bright minds be made by playing chess or other strategy games such as go/ gomoku, checkers, or chinese checkers? I've always believed in the latter (because of tabula rasa), and I think that this school program shows some concrete proof of this.

If you are a parent with young children, consider teaching them any of the strategy games mentioned above, as early in their life as possible. Play for fun, even if you yourself are not good at the game. Then let them decide on their own, later in their life, if they want to continue. Child prodigies are that because they started early, while their minds were still developing.

Links: Chess strategies sharpen study skills.

(c) Copyright: 2006-present, Raj Kumar Dash, http://getyergameon.blogspot.com/

Technorati Tags: games, strategy games, chess, analytic games

The Mathematics of Dovetail Shuffles - Card Tips

Sometime in the 1990s, I came across a story that stated that it takes exactly 7 perfect dovetail shuffles to completely randomize a deck of cards.

Apparently, this method is so randomizing that it beats most computers' random number generators.

Don't Feel Like Poker Today, Try Backgammon

The Poker Web (links below) has a detailed comparison of the similarities between poker and backgammon. The first point is that both games require a great deal of skill, but are subject to some chance as well. For this reason, says the article, they're both great gambling games.

Years ago, when I was honing my backgammon skills, I read in my paperback reference that the top players around the world included various royalty, including a then well-known young crown prince of a small nation. I've not found my book in years, but I remember reading that top tourneys had 6-figure grand prizes - which in those days was a lot.

Heavy duty gamblers also relied on the "doubling cube" to up the ante. There are stories of pirates playing backgammon who won vast fortunes with the doubling cube.

Being a fan of both poker and backgammon, I have to say that while I like backgammon more, it's always been easier to find partners for a game of cards than for backgammon. Very few people that I've encountered understand the game. While the rules are relatively simple (as is the case with poker), skills in backgammon take time to acquire, with the "back game" usually being the bane of the newbie.

If you're interested in playing free backgammon online, The Poker Web's article has a link to "Gammon Empire". It's repeated below for convenience.

Links: The Poker Web - The Similarities of Backgammon and Poker; Gammon Empire.

(c) Copyright: 2006-present, Raj Kumar Dash, http://getyergameon.blogspot.com

Welcome To Get Your Game On

This blog is about games that require both strategy and chance - board games and card games. This includes, but is not limited to, poker, backgammon, chess, checkers, othello, go, gomoku and more.

I do write for a poker blog, but the entries here will be original content. I do plan to build up this blog, move it to its own domain, and create an online community - but that's for the future.

cheers