Twincognito Tips

1. Make each cell white or black.

2. No two black cells may share an edge.

3. All white cells must be connected to each other through their edges.

4. No two white cells with the same number may be in the same row or column.

Be sure to read the Japanese-Crossword-Puzzle-Like Puzzle Tips.

So, these puzzles are actually really hard to make, so I rarely ever make them (I've only made one at the time of writing).  I wouldn't be surprised if there's some trick to making them, but I don't know it.  The example puzzle actually isn't that good.

Anyway:

Theorem 1: If a cell is white, all cells in that row or column that are the same number are black.

This is just an extension of Rule 4.  So, say you have this:

(I'm not going to write all of the numbers that you usually have in twincognito in these examples.  Most of the numbers in a twincognito puzzle are useless anyway.)

With this theorem, you can write this:

I would suggest that with every white cell you make, you look around the whole grid for another number.

Theorem 2: If three cells in a row have the same number, the cell in the middle is white while the others are black.

So, this:

means this:

Theorem 3: If there is a cell with two of the same number on opposite sides, that cells is white.

If you have something like this:

If the cell between them was black, both eights would be white (which is bad).  So, the cell is white, like the theorem states:

Theorem 4: If there are two cells of the same number next to each other, all other cells of that number in the same row or column as the two cells are black.

Consider this:

If one of the top two is black, the other is white.  No matter what, that five down there is black:

I'm not going to state this as a theorem, but consider something like this:

If one of those cells is white, it will make the other black, which will make another white, etc.  In the end, there's only these two possibilities for it:

Both R3C2 and R3C5 are white in both solutions, so we can write this:

If it's longer, then you can still reason out the same thing.

Also, if it's against a wall, you can figure out more:

The second solution shown above chokes out a white cell on the wall.  Thus, the only solution to this is this:

Having just two against the wall is something similar.  You should be able to figure that out.

I can't think of much else to say, so example puzzle time!

So, we use Theorem 2 on those threes:

Now, I'll mark each cell white, and with each one I'll see if it makes another cell black by Theorem 1.  First, all of these don't do anything:

The three in R3C4 makes the three in R3C8 black:

The seven in R3C6 makes the seven in R5C6 black:

Now we have a whole bunch more spots to make white.  These don't do anything:

All of these whites make these black:

Now we have a whole bunch MORE to do...

The six being white makes the other six black:

The four being white makes another four black:

We could keep on going like this, but it won't show anything off.  I'm going to purposefully try to figure things out other ways to make this more interesting.

We can use Theorem 3 on this six here because there's two fives:

Look at the fours and fives at the bottom.  They are one of these two:

They both have R9C4 and R9C7 the same, so they're both white.  That five being white also makes two other fives black:

We can use theorem 4 on R4C9:

Now, consider those eights, fives, and nines to the right.  They can only be these two things:

The first one chokes out an area of whites, so it must be the second:

There's not much else to show off, so I'll just put this thing on autopilot.  I'll just make white cells and any associated black cells:

Now the last two are a little less obvious, but they need to be white so that all whites are connected:

Just so you know, this is NOT how these puzzles usually solve.  This puzzle is just a really bad puzzle.  Twincognito is usually one of the hardest puzzle types out there.  I'm just really bad at making them, and this example was my first attempt at making one.  If you want to try better ones, solve my actual Twincognito puzzle or mathgrant's Twincognito puzzles.