Sudoku : Math and stat connections
Logical skills are required rather than purely mathematical skills
for solving Sudoku.
For example, the game could easily be played with 9 colours,
or 9 animal pictures, or 9 words, rather than the numbers 1-9.
[The solution to the puzzle on the right can be found here. ]
There is however a close connection with Latin squares in Mathematics, which themselves are very important in Experimental Design in Statistics. Latin Squares have been known about for a long time (since the 18th Century when the great Swiss Mathematician Leonhard Euler (1707-1783) investigated them). In fact, a Sudoku grid is a type of Latin square, but with about 2/3 of the numbers missing.
Euler's problem: (from Mathworld ): How can a delegation of six regiments, each of which sends a colonel, a lieutenant-colonel, a major, a captain, a lieutenant, and a sub-lieutenant be arranged in a regular 6 x 6 array such that no row or column duplicates a rank or a regiment? The answer is that no such arrangement is possible. Euler conjectured it was false - and it took 118 years to prove it! A related conjecture was only sorted out in 1959!
From Mathworld: Euler was the most prolific mathematical writer of all times finding time (even with his 13 children) to publish over 800 papers in his lifetime. He won the Paris Academy Prize 12 times. [...] When asked for an explanation why his memoirs flowed so easily in such huge quantities, Euler is reported to have replied that his pencil seemed to surpass him in intelligence.
How many different Sudoku grids are there?
An enormous number! Apparently the 21 digit number 6,670,903,752,021,072,936,960 - see this technical report if you really want to know why!Many Sudoku published puzzles are symmetric about a rotation of 180 degrees, but they don't have to be. There are many programs around to solve Sudoku (see the links page). It's something a computer can do really well by brute force (in particular a back-tracking algorithm can be programmed quite easily - see our Sudoku solver written in R ). It's more of a challenge to write a faster program that solves it in the way that a human does.
There's much more fun in trying yourself to use more satisfying logical methods.
There's a jungle of information on Sudoku on the web - here are some sites, with plenty of puzzles (potentially 6.67 x 10^21 of them!).