## Yajisan-Kazusan (and how to solve them)

(Eingestellt am 5. Juli 2020, 12:00 Uhr von Carrick22)

Yajisan-Kazusan

Shade some cells according to the following rules :

• Black cells must no be orthogonally adjacent.
• Cells with numbers can be blackened.
• A number in a white field indicates the number of black fields in the corresponding direction.
• A number in a black field is irrelevant and does not necessarily indicate the correct number of black fields.
• All white cells must form a single orthogonally connected area. Example :

Since I wasn't able to find numerous puzzles of this type nor a complete guide on how to solve them, here is a puzzle by Mokuani and how to solve it. (The real puzzle is at the bottom)

First of all, consider the following : The 3 in the last column is an impossible value for the cells it is pointing. These "impossible" values should be tracked down as it's generally the first step to solve such puzzles.

After marking the neighbouring cells as white, we get some white fields with numbers. As they are the strict maximum of black cells and can only be filled in one way, we can fill those in.

Repeating the same procces should get you here.

Let's take a look at another rule : "All white cells must form a single orthogonally connected area". At this point in the puzzle, even if we cannot go further with the numbers, we can rule out squares that would break this rule.

Now, take a look at column 2. The last number is pointing at only 1 black square and withe cells. As such, it cannot be fulfilled and can be blackened.

Following the rules aforementionned, we get to this point.

Here is now a trick I call ladders. You can see that the 2s in column 6 will have to alternate between black and white. Here are the two possibilities :

But using the first configuration will create two separate white fields :

Thus only the second way of filling the black squares works. This is a very useful tip to avoid getting stuck when you believe there are multiple solutions. Let's write that down.

Using the same "ladder" principle you can fill the last 6 black squares. You solved the puzzle !

The following puzzle uses another 2 tricks for solving (one when starting), although they can be omitted by working through contradictions.

Lösungscode: Row 7, followed by row 10. Use "1" when shaded and "0" when white. The online solver should notify you when the puzzle is solved.

Zuletzt geändert am 5. Juli 2020, 12:28 Uhr

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### Kommentare

am 5. Juli 2020, 20:58 Uhr von Carrick22
By the way I should mention that more of my puzzles can be found here : https://www.reddit.com/r/CarricksPuzzles/

These are usually puzzles that can't make it here (difficulty/ not pretty enough), or would be spam (when I release like 16 of them at once).

Zuletzt geändert am 5. Juli 2020, 14:27 Uhr

am 5. Juli 2020, 14:26 Uhr von Dandelo
https://www.janko.at/Raetsel/Yajisan-Kazusan/index.htm

am 5. Juli 2020, 13:58 Uhr von Puzzle_Maestro
There are Yajisan Kazusans aplenty here: https://deceptivepuzzles.wordpress.com/category/yajisan-kazusan/

Zuletzt geändert am 5. Juli 2020, 13:24 Uhr

am 5. Juli 2020, 13:12 Uhr von Zzzyxas
There's a mistake in the example: In the first picture are two 3s (rows 2 and 3) which became 2s in the following pictures.

- Should be fixed.

 Schwierigkeit: Bewertung: 87 % Gelöst: 62 mal Beobachtet: 0 mal ID: 0003T1

Lösungscode: