# Solve the pattern! (game)

Okay, so this is based off of https://www.chiark.greenend.org.uk/~sgtatham/puzzles/js/pattern.html

And, my cousin made a random pattern and gave it for me to solve.

Unfortunately, the logic is beyond me. So i'll give it to for you guys to solve!

Rules

You have grid of squares, and you have to fill all the squares black or white.

Beside each row are the lengths of the runs of black squares in that row.

Above each column are the lengths of the runs of black squares in that column.

Also, the numbers will appear in the order the runs appear (see below)

 For example, if the row looks like this: ■■■■ ■■   ■ ■  ■■, then the numbers at the side
of the row will be 4 2 1 1 2. Note that the numbers appear in the order the runs appear.


If you need to, alt+254 is a black square, and alt+255 is a white square.

So here is the puzzle that was sent. My cousin says there are 3 solutions!

        1  1
11111221 11
111111122221111
121111111121221
_______________
12|
123|
7|
34|
15|
1118|
1112|
223|


And here's an image:

## Logic

By logical deduction I've got as far as this:

(black squares are filled, grey are definitely not filled, white are still unknown)

I think that's as much as we can do with pure logic, so here must be where the three possible solutions appear.

## Number 1

There's an L-shaped hole in the middle. If we assume the middle cell of the L is filled, we get the following solution:

## Numbers 2 and 3

Now we assume the middle cell of that L is not filled. The two solutions arising here are almost identical, so I'm showing them in one image:

The empty $$2\times2$$ square near the top must have two diagonally opposite squares filled and the other two empty, but it could be either way round.

• Wow. Wow. How did you do it so fast? – Alto May 27 at 20:43
• @Alto There's only a limited number of types of logical step necessary to solve these puzzles. I got a lot of practice with these around 15 years ago. There were a few (2 or 3?) points in the solving process when I had to pause for a while and hunt for the next step, but once you get an "in", there's usually a small avalanche of deductions following it. (Hmm ... maybe I should write a tutorial for solving this type of puzzle, like I did before ...) – Rand al'Thor May 28 at 15:23
• @Alto - it sounds like you are not familiar with nonograms. There are several free nonogram apps with puzzles like these. The puzzles can yield a random pattern, but most of the apps result in a picture when you are finished - sometimes a very detailed one. I thought you might enjoy this type of puzzle - I do – Pugmonkey May 28 at 18:06