Daily Binairo
Rules
Click on cells and fill the board with white or black circles. To choose the correct color follow these rules:
- No more than two of the same colour next to each other
- Each row and column must have the same number of coloured circles
- In the non-Plus version no two rows or columns must be the same
- In 'Plus' a '=' symbol between two cells means these two cells are the same
- In 'Plus' a 'X' symbol between two cells means these two cells must be different
Guaranteed a single solution!
Now with Print option
Comments
Email addresses are never displayed, but they are required to confirm your comments. When you enter your name and email address, you'll be sent a link to confirm your comment. Line breaks and paragraphs are automatically converted - no need to use <p> or <br> tags.
... by: FHessel
May I make a suggestion?
As I noted below the 8x8 Binairo Plus, the 8x8 binairos have an important disadvantage: there is almost no chance, that an overall number of 3 or 5 blacks will occur, and if it does, then it can be recognized qute fast. Consequently the number of black cells is not really a degree of freedom, as it should be based on the concept of the puzzle.
Using 9x9 instead would change the whole picture.
In numbers...
8x8:
2 blacks - 1 possible pattern - 0 valid boards
3 blacks - 16 possible patterns - 16 valid boards
4 blacks - 34 possible patterns - 4.111.116 valid boards
5 blacks - 16 possible patterns - 16 valid boards
6 blacks - 1 possible pattern - 0 valid boards
9x9:
3 blacks - 10 possible patterns - 0 valid boards
4 blacks - 45 possible patterns - 5.116.926 valid boards
5 blacks - 45 possible patterns - 5.116.926 valid boards
6 blacks - 10 possible patterns - 0 valid boards
Using 9x9 would not only more than double the possible number of puzzles, it would also introduce a real choice between 4 blacks vs 5 blacks, each having equal probability.
This could open the way for harder puzzles which not only @Thinkist hopes for.
WB
BW
or
BW
WB
except when swapped, there are (1) still no more than 2-in-a-row for W or B, and (2) still equal numbers of W and B in a given row or column.
Also, one of standard Binairo's rules actually requires the grid size to be even, so 9×9 wouldn't work, though 10×10 (12×12, etc.) would.
Really all this is why I (and others, actually) kinda suggested something like a "weekly diabolical" or the like.
... by: Denk-mal
Thanks for that.
The only thing I would like to see is that the check would only shows IF something is wrong and not showing WHAT is incorrect on the field.
... by: Thinkist
And so, my request: some harder puzzles that use these (Weekly "Extreme", perhaps?). Also, no Hint button for these either.
Also, a fun combinatorics question for anyone reading this: how many possible Binairo solutions (i.e. solved grids) are there for a given 2n by 2n grid (NB this does not even begin to touch on the number of possible puzzles...).
I will have a look at the code again, maybe there is something I missed.
I do know that the regular Binario should have the rule about no rows or columns being identical but that this is not a rule in Binario+. By that I mean the generator enforces the no-duplicate rows/columns (I think!) but it is not a necessary rule to solve the puzzle. It’s very niche so I don’t think people will be up in arms either way
Not sure how to turbo charge the creator to make extremes. I don’t think the spectrum is wide enough or has a long tail like Sudoku. Or maybe I can change the scoring to do that.
Is a good combinatorics question!
... by: nono
... by: Thinkist
This reminds me of the many like puzzles in this game called Islands of Insight (https://store.steampowered.com/app/2071500/Islands_of_Insight/), where many different rules can be applied to make many different kinds of black-and-white puzzles in this game's Logic Grids.
For example, Binairo can generally be coded in using a couple of "Don't make this pattern" rules and some Darts.
Anyway, back to the webpages. For those using a mouse: left-click to add black, right-click to add white. Both options cycle between black, white, and empty upon subsequent clicks. I mention this because these precise details aren't exactly in the Rules. Also, in Islands of Insight, one could simply left-click to add black, and instantly right-click to change it to white without the need to erase a cell (or vice versa), and it would be nice to have that behavior here as well.