The mathematics behind Sudoku

Sudoku is a puzzle that is based on a mathematical construct called Latin Square. Click here for a discussion in Wolfram Mathworld.



I just discovered today (November 1, 2006, see the same link above for the reference) that the question of counting different Sudoku puzzles (the 9x9 case) was solved just this year, January 2006, by Ed Russell and Frazer Jarvis. They counted 5,472,730,538 "essentially different Sudoku grids". That's around 5.5 billion different possibilities of arranging the numbers. That means there are more than 5.5 billion Sudoku puzzles that can be constructed by hiding grids in many different ways.

Ton, naunahan na pala tayo kahit nagawa pa natin ito noong Summer. Hehehe.

Puzzle in Table format

8						6
				4		1		5	7
2				5				6		4
7		8							3
	5							8		6
6		3				4				9
	9	4		7		5
				1						7

Squiggly Sudoku

Have you tried this? Instead of 3x3 boxes, the numbers are grouped in squiggly boxes. In the following problem, the central box is still the old 3x3 square. Good luck!

News: Philippine Daily Inquirer joins the Sudoku craze

Yes, it is only this year (not sure on the exact date but maybe around June) that a major daily in the Philippines (Philippine Daily Inquirer) has introduced a section on Sudoku puzzle. I heard the news first from my wife who is, ironically, in Hong Kong, where a daily (South China Morning Post) has introduced me to this puzzle last April.

The other day, I discovered that a friend is crazy over Sudoku in PDI. I shared to him how this puzzle has caused chaos to many people in London when it was first introduced there way back 1920s (not really sure on this but I'm sure it is not later than 1950).

Last summer, after my short visit in Hong Kong, I organized a computers group in line with our research in physics. Well, the members are not physics majors so I gave them the Sudoku challenge as our first project for the group. I just wanted to gauge their skills and enthusiasm. So far we have not finished the software that produces Sudoku puzzles but we already have an idea how. We have not met since this semester opened.

I think I have to convened the group as soon as possible.

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*Edited November 1, 2006

I can't remember now how I arrived at the year 1920s when Sudoku was first introduced as a puzzle. But that notion is wrong if the article in Wolfram Mathworld got it right that the puzzle was published by Garns in 1979 [1].

[1] Garns, H. "Number Place." Dell Pencil Puzzles & Word Games. No. 16, May p. 6, 1979.

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