Binary Puzzles

Here is another novelty: Binary Puzzles, also known as TAKUZU.

Binary Puzzles are played on square grids of any even size: 6×6, 8×8, 10×10 etc.

Your goal is to fill the grids with 0s and 1s, following these simple rules:

1. There can be at most two 0s or at most two 1s next to each other, horizontally or vertically. So, 00 and 11 are ok, but 000 and 111 are not ok; also, 010 and 101 are totally fine.
2. There must be an equal number of 1s and 0s in each row and in each column.
3. Two columns cannot be completely the same. Neither can two rows be the same.

And that’s all!

Binary Takuzu Puzzle: 12×12 WARNING: DIFFICULT!

(click to download or right-click to save the image)

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sudoku variants and other puzzle books

To see the solution to this puzzle click here

How to solve Binary Puzzles

Well, the basics are very simple and follow directly from the rules just explained. Let’s see these examples:

? 0 0 ? 1 ? 1

From 1st rule we conclude that the first and second “?” must be 1. Also, from the same rule, the third “?” must be a 0. That’s easy.

? 1 0 1 1 0 ? 1 0 1

There are already five 1s in this row of 10 cells. Therefore, in order to abide by the 2nd rule, the remaining two spots must be filled with 0s!

0 1 0 1 1 0 0 1 0 1
1 0 1 0
0 1 0 1 1 0 x xx 0 1

This is only a part of a puzzle. See how first row is completed and the 3rd row is almost the same as the first one. If x=0, then because of the 2nd rule xx=1, but then the 1st and the 3rd rows would be completely the same! Therefore, x=1 and xx=0!

Finally, let’s look at a slightly more complex position:

1 0 0 1 0 0 ?

Here, there are already four 0s filled in. There can be only one more 0 in this row! Can the “?” be “0”? No! Why? Because the three blank cells would all have to be 1 and since they are all adjacent, this would be against the 1st rule. Therefore, there must be a “1” in place of the “?”.

Got it? Every time there is only one occurrence of a digit missing in a row, check where it can or cannot go!

What do you think?

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4 Comments

  1. Scott Urman
    Posted October 3, 2013 at 12:41 pm | Permalink

    Tricky! I like it. I’m down to 8 unfilled squares at the moment. 😉

  2. Roland
    Posted October 7, 2013 at 12:42 am | Permalink

    I really did enjoy this binary puzzle. New challenges, a new look at numbers, but doable.

  3. mumdigau
    Posted October 10, 2013 at 3:01 pm | Permalink

    Seem to have found a 2nd solution:

    0 1 1 0 1 1 0 0 1 1 0 0

    0 0 1 0 1 1 0 1 1 0 1 0

    1 1 0 1 0 0 1 0 0 1 0 1

    0 0 1 0 0 1 1 0 1 0 1 1

    1 1 0 0 1 0 0 1 0 1 1 0

    1 0 1 1 0 1 0 0 1 0 0 1

    0 1 1 0 1 0 1 0 0 1 1 0

    1 0 0 1 1 0 1 1 0 1 0 0

    0 1 0 1 0 1 0 1 1 0 0 1

    1 0 1 0 1 1 0 0 1 0 1 0

    0 1 0 1 0 0 1 1 0 1 0 1

    1 0 0 1 0 0 1 1 0 0 1 1

    I can’t see any rule violation. Did I miss something?

    • Posted October 11, 2013 at 6:04 am | Permalink

      Seems like you did miss something. Your columns 6 and 9 are identical, which is against the rules. 🙂 Sorry 🙂

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