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# Two-person Sudoku

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Here's an idea for an entrepeneur.

Create a two-person Sudoku game. My idea is this:

Instead of numbers, use colors. It looks nicer, and I think it would be more fun.

Have an electronic board that generates the puzzles and keeps track of each player's time. When the game starts, it's the first player's turn. His clock is running. He selects a color and places it on the board (by pushing on the spot--the electronic board will sense both the color he picked and the place he marked). If his placement is correct, it is the other player's turn. The other player's clock starts, and he selects a color and places it on the board. Play continues until one player runs out of time (loss) or makes an incorrect move. If the puzzle is solved with neither player losing, it is a draw.

By the way, I think that the linked article does not talk about my strategy. I am number-focused, rather than cell-focused. That is, I look for 8's, and then try to find ways in which the existing 8's force a particular cell to have an 8.

CATEGORIES: Game Theory

Ivan Kirigin writes:

Ideally, I would like to take notes of three different types.

Within a 3x3 cell, use one type to mark all the possible positions of each number. After this, if there is any position with a single number in it, that must be the number's location.

Similarly, for each row, with a different type, mark the possible positions of each number. You can also fill in numbers this way.

Similarly, for each column, with the 3rd type, fill in all the possible positions.

For a given 3x3 cell, only where all three types intersect for a certain number can that number go there.

In this fashion, you can complete even the hardest sudoku in under 5 minutes, though it is a bit mechanical.

When playing on a computer, I only use the first type of markings, as they are easier to control.

Within a 3x3 cell, use one type to mark all the possible positions of each number. After this, if there is any position with a single number in it, that must be the number's location.

Similarly, for each row, with a different type, mark the possible positions of each number. You can also fill in numbers this way.

Similarly, for each column, with the 3rd type, fill in all the possible positions.

This is identical to simply evaluating each's cell's possible values in all three dimensions simultaneously (i.e., what numbers could be in this cell?), except more tedious.

In this fashion, you can complete even the hardest sudoku in under 5 minutes, though it is a bit mechanical.

As stated in the linked article, simple elimination is not sufficient to solve the higher difficulty puzzles.

To the OP: Colors are a bad idea...given that a sizeable portion of the male population exhibits some form of color deficiency, finding 9 colors with sufficient contrast would prove difficult. As a member of the afflicted, I find that most games involving more than 4 colors are lost on me; there will invariably be a yellow/green or blue/purple pair that I cannot easily distinguish.

Ivan Kirigin writes:
As stated in the linked article, simple elimination is not sufficient to solve the higher difficulty puzzles.
Hmmm. Maybe I should try some harder boards!

This app is what I currently use. I would recommend it.

Further, I would approach this problem from my background: how would a computer do it. I know that takes the fun out of it for most people, but when you're the one writing the code, I assure you, it is quite satisfying.

Here, a hybrid of the elimination method, and trial and error are needed. Guiding the search space for the latter by the former would be quite efficient. I might just add this to the long list of projects on my queue. [or is it a stack :-P]

John S. writes:

Actually, a game similar to this already exists, but without the time element. My mother is a Sudoku fan, so when she visited for Thanksgiving I purchased the game and we played it. It was no fun at all! The game consists of a board (looks just like a blank Sudoku grid) a bag of Scrabble-like tiles (with numbers printed on them instead of letters) and a book of puzzles. You set up the puzzle on the board, and then the players take turns, putting down numbers to complete the puzzle.

I don't know about you but I have to stare at a Sudoku puzzle for a long time before I put down a number (depending on the difficulty of course). Sitting there with someone else, waiting as they think, is rather boring.

I find that Sudoku is a great way to pass the time on long plane rides.

writes:

John, in the game you bought, how do you know which player made the mistake--or are you each playing on your own board?

writes:

I like your idea, except I prefer something more interactive.

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