Sudoku frustrates me. I can usually do the easy ones but have never made progress with any of the more advanced puzzles.
Not that I’ve ever spent much time on it because I never thought it was worth the effort when solving Sudoku seemed to owe more to luck and probability rather than brain power.
But I was wrong, it’s not jsut luck. The answers can by worked out by applying logic and there is a formula for solving the number puzzles.
James Crook, an emeritus professor in South Carolina, will be publishing his “pen-and-paper algorithm for solving Sudoku puzzles” on the web-site of the American Mathematical Society. While his paper runs to nine pages of detailed argument, the algorithm boils down to five logical steps.
If it takes nine pages to get the logic, I’d rather leave it to luck. However, if you’re more enamoured with numbers than I am and want to apply the formula, you can read the paper here.
Hat Tip: Larvatus Prodeo
The formula Crook presents in his paper isn’t new.
Basically, if you want to solve Sudoku the laborious but straightforward way, when you get stuck, guess. If you guess right, good. If you guess wrong, you’ll reach a point where the sudoku rules can’t be fulfilled, and you go back to where you guess and try another possibility.
The best place to take a guess is where there are only two possibilities to go in a square.
Sudoku is just simple logic. You don’t need a formula, just an analytical, logical approach personally, I find it relaxing – and I hardly ever guess.
And, yes, my wife and daughters think my fascination with sudoku is weird.
“You don’t need a formula, just an analytical, logical approach . . .”
That explains why I don’t get it.
I agree with Robert. The ‘formula’ in that paper doesn’t do anything for me.
It essentially gives one way of finding moves, and if that way doesn’t provide a move, then you guess. If you get stuck later on, go back and make a different guess. I suppose you could call that that an algorithm but it’s a pretty useless one, especially when there are other ways to avoid guesses that it doesn’t include.
As MacDoctor said, guessing should be rare.
Luck isn’t really part of it, and certainly not probability.
Welcome to the Gang. Useless for Sudoku.
Basically there are diffrent ways to solve each square and the methode that solves that square is dependant on how you got to that point, there are at least 3 possibilities that I can think of to solve the squares one is the process of elimination by making sure the number chosen number is unique to that vertical and horizontal this can only be done by observing other numbers which will eliminate all other squares except for the one u need to put your number in, two by observing what numbers are left unacounted for in a series of verticall or horizontal then u can figure out say for example if you have 3 squares that you know what numbers need to be there but are not sure of the order then u can use the rule of 3 by looking at the 3 other boxes to see what numbers are left to be filled out and if there is a box that holds one of the three numbers where the other two boxes left hold all 3 other numbers then u can place this unique number in that square, the third methode if there is one i forgot lol but it is amaizing the ways ur brain realises it needs to work it out,,,I am not sure if there is a formula or perhaps some sort of matrix theory out there but I have come up with a way that helps you solve it a little bit faster by not having your brain go crazy by trying to remember every missing number, I always make a grid or tic-tac-toe grid that has the 9 boxes without the squares and fill in the missing numbers into each empty box , this is very helpfull as it keeps your brain free to play the game without having a mneumonic memory, I then go through every number on every box which pretains to the same box on the sudoku puzzle one at a time till I eliminated as many numbers as I can using one methode of elimination ,, you then realise that u get to a point where you need to use diffrent methodes of which I spoke of but the tic-tac-toe box stratedgy will always be there to help guide you throughout the whole game, remember to scratch out the numbers as u find them. But this strategy which I share with you is very helpfull and you will thank me if you havent already figured this out. It usually takes me longer than 30 min to solve a puzzle but thats because I need practice, the important thing here is that I found a way that always helps me solve the puzzle no matter what.
happy sudokoing
I just remembered the third methode, it is also by observing other numbers that help eliminate most squares although you might be left with two possible squares instead of one, you may be able to eliminate one of those squares by knowing if the other possible number that can be the only other one that goes into one of the two remaining squares( you will find this other number thanks to the numbers left in your tic-tac-toe strategy guide,,see I told you it helps in more ways than one) you then see if there is a surrounding simillar number be it horz or vert then if your lucky you will not only know how to find one square but you will have the anser for two squares. as far as the second methode I spoke about I may have made a mistake in explaining the logic of it but I think that way works out as well but just in case I will give another example,,suppose you are looking at a vertical column that has say three squares that are missing,two squares are in one box and the other square in the other box lets say these three numbers are 7 ,4 and 2 , now you can look at your tic tac toe thing to see wutt numbers are left for those boxes and realise in one box that 7 and 2 are there still and in the other box there are 7, 4 and 2 remaining out of whatever other numbers are left,,,now you can be ceratin that you must put that 4 in that square of that box and if you were only trying to find two squares instead of three than you would already know where that remaining number would go, as far as the 7 and 2 left you will realise them in time specially if you just found an extra number like the 4 then it would help find something else which will eventually help you solve for 7 and 2.