When we were in Paris in April (yes, April in Paris!), I read Le Figaro every day to catch up on the election news (Sarkozy vs. Hollande vs. Le Pen) and to help try improve my French comprehension. While the latter was fairly successful, I was diverted by the puzzles page. Not only was there a Sudoku puzzle, but there was another puzzle I hadn’t seen before called Takuzu.

It’s a fill-in-the-grid logic puzzle, but unlike Sudoku you can only use 0s and 1s. Here’s an example from binarypuzzle.com, tagged as “easy”:

There are some rules to follow too:

1. There must be an equal number of 0s and 1s in each row and column. Since this example is an 8×8 grid, that means there should be four 0s and four 1s in each row and column.
2. There cannot be more than two 0s or 1s next to each other.
3. The layout of each row and column much be unique; that is, no two rows or columns can be the same.

It’s quite fun to do. Let’s take a look at solving this one. I generally start off by blocking off the runs of two 0s or 1s (applying rule 2).

As you can see, this oftentimes produces more runs of two, so you can apply rule 2 recursively.

Take a look at row 5 now. Notice that it already has four 1s. By an application of rule 1 you can fill in the remaining two cells with 0s. Column 4 is even simpler to complete using the same rule. However take a look at row 3 for an example of applying some lateral thinking. In that row, there are two copies of the following pattern: 1 <empty> 1. Consider putting a 1 in the empty cell: you’d end up with three 1s in a row, a violation of rule 2. So, that empty cell can only be a 0. In this example there are several examples of this pattern (don’t forget the columns as well).

And this, of course, gives more opportunities to apply the first couple of rules. And, in this case, we can finish the puzzle quite quickly.

As this is an easy puzzle, we didn’t have to use rule 3. Generally, it’s only the more difficult puzzles that rely on this particular rule.

If you want to practice, I’d pop on over to binarypuzzle.com and try a few out. The hard ones require a bit more lateral thinking than I’ve shown here.

If you have an iPhone, there are also several apps available in the AppStore that implement the game. Unfortunately the name Takuzu is not widely known (it seems to be limited to France and Le Figaro especially, and sounds like a Japanese weed to me) so you have to search for “binary puzzle” or even “binary Sudoku puzzle”. Here are a few:

• Binary Puzzle (the new Sudoku) – I bought this and didn’t like the interface. The cells can sometimes be difficult to read since the contrast is all screwed up. I gave up on it.
• Binary Sudoku Puzzle HD - The Original! – I bought this one too. Looks much better than the above, but, boy, the touch point –> cell conversion routine is whacked out. I gave up using my finger and used a stylus instead since I was getting too many false readings. The problem with it is, once you’ve completed all the puzzles (there are 135 in all), all you can do is try and improve your scores. The developer doesn’t seem to have provided any more puzzles as an upgrade.
• Bitsy Pro – just bought this one to try out. The interface looks refreshingly simple.

Anyway, have fun!

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