Binary Puzzle

If you like puzzles like this, you should check out Nikoli (http://www.nikoli.com/en/). They're a Japanese gaming company with a bunch of puzzles online. They don't have this particular puzzle, but they have similar ones, like Hitori (http://www.nikoli.com/en/puzzles/hitori/).

Last year my desk calendar had a bunch of these sorts of puzzles, so some things I learned:

Any time you see "0..1" you have to have a 0 and 1 between them. This is useful since each row/column must have the same number of 0s and 1s (5 each in your puzzle). So counting from (1,1) as the top left, what does (6,3) have to be? You may not know the position of all the 0s and 1s in row 6, but you have most of them accounted for because of this specific relationship, and one free space. Figure it out and you get at least 5 positions resolved.

Keeping in mind that the number of 0s and 1s have to be the same, find rows where the number of 0s or 1s is near the max but the other is far from it. Your row 3 is one such location. There has to be one more 0 and three more 1s. Since the 1s can't all be together, you get some constraints on the outside of that four space gap "010...010". If you put the 0 on the outside of the gap, the 1s must be all in a row which is invalid.

Your column 2 offers a similar situation. 4x0s and 2x1s. (from the top) ".01001...0". Where can the one remaining 0 go, or where can't it go?

Repeating this I can spot about 15-20 spaces that'll be filled in very quickly, and the rest probably falls into place after that.

Nice! For people who don't get the reference in the name Zanellati gave,

https://en.wikipedia.org/wiki/Tohu_wa-bohu

Edit: I didn't realize that, as Wikipedia says, this Hebrew phrase is used as a loanword in several European languages to refer to disorder, which in turn explains why Tatham called it "Unruly".

I got past that and then realized every row/column needs to be unique.

> 3. Add random elements to an empty grid. Eventually the grid will have one or zero solutions. If zero, backtrack. If one, stop.

You can use that approach to make a multiplayer version of Sudoku. Start with an empty grid, and the players take turns filling in numbers. If a player on their turn is unable to fill in a number without making an on-the-board violation of the non-duplicate requirements for rows, columns, and sub-squares that player is eliminated.

Note that this can be played without a computer, because elimination happens when there is forced to be a duplicate actually on the grid.

If playing on a computer a more difficult multiplayer Sudoku is possible. After every move the computer checks to see if it is still possible to complete the grid according to Sudoku rules. If it is not, the player who made the last move is eliminated, and their move is erased.

Note that a similar approach can be used with many other single-person puzzles. For example, the 8 queens puzzle as a two-player game becomes the players take turns placing queens on a chess board, and the first player who places a queen that is attacked by an already placed queen loses.

As with Sudoku, two-player 8 queens could be done without a computer with the game terminating when a queen is placed on the board that is attacked, or it could be played with a computer with the game terminating when someone places a queen that makes it impossible for the game to end in a draw.

In early 2011 at work we were brainstorming mobile app ideas, and I suggested both of the above but there was not much interest. They have been on my "todo" list for whenever I get around to learning iOS and/or Android programming...but I've had "learn iOS programming" on my list since 2008, so I doubt I'm ever going to get around to it.