Nonogram (IllustLogic)

Key to solution

Beginner Level (1)

Last updated: 28/April/1997
Translated: 22/April/2000

I'd like to show you some knowhow to enjoy Nonogram in this section.

If you click here, the sample puzzle used in this section will be shown in a new window and you can solve the puzzle as you read this section.

This is what the puzzle looks like when you start solving it. You are going to reveal hidden picture in the grid with the clues given at the ends of each rows and columns. The clues tell the number of consecutive black squares.

I am going to explain how to solve Nonogram efficiently using the clues placed to the left of each row and on top of each column. This page is for entry-level beginners.

It is helpful to look at one line (a row/column) at a time to solve the puzzle. Look for a line with clue containing large number.

In this example, the largest clue is 6 at the bottom row. The following image shows only this line.

You must place six contiguous black (solid) blocks somewhere in these ten blocks. So, let's consider two cases, when the solid blocks are placed at the ends of the line (left/right). The images are shown below:

Note the middle two blocks are filled in both cases. This is the overlapping part. I picked only two cases to find overlapping part. If you are interested, you can make sure these blocks will be always filled in all other cases.

The result in the whole grid will appear as in this figure.

You can ignore the light blue parts in figures. This is just a function of my Nonogram program. It indicates which block is currently pointed by mouse.

Since two solid blocks are determined, it may help to determine some other blocks. How can they be found?

Look at columns containing these solid blocks.
The clues for these columns are (1,2,1,1) and (1,1,1,1,1). They actually appear in vertical order in the puzzle.

The black blocks correspond to (1,2,1,1) and (1,1,1,1,1) respectively. Both blocks should have length of 1. Therefore, there should be blank blocks on top of those solids as in this figure.

Now, if you leave a blank block unmarked, you can't tell if it is decided to be blank or still undecided. So, when a block is determined to be blank, place a dot as reminder.

Also, click on clue numbers that have been decided to mark with gray. This helps you to keep track of your work.

When you look for next line to solve, there is an important principle:

Look for row/column, which has larger sum of clue numbers.

Try checking the sums of clues for rows. Followings are sums of clues for the top three rows:

  3+3 = 6
  2+4+2 = 8
  1+1 = 2
Among all sums, the second row has the largest sum and looks like it may yield some solution.

Starting from the leftmost block, try putting two solid blocks, one blank block, four solid blocks, one blank block, and two blocks in order.

This pattern fills this line. It is clear there isn't any other way to fill it. So, this line is finished.

Did you notice the calculation (2+4+2 = 8) was incomplete? Considering the blank blocks to be placed between solid blocks, the complete sum will be 10 (2+1+4+1+2 = 10). And it fits the width of the line.

The practical principle is to find a clue, which seems to make larger sum and contains larger number. You don't have to hustle calculating everything like computer.

Now, look at the first (left) column. Following image (a) shows only this column.

Next, imagine two cases to place the solid blocks: when they are placed
(b) as high as it can be, and
(c) as low as it can be.
Since a black block in the images is already decided, solid blocks won't go lower than (c).

The color (orange) used in these figures appears when you are in the try mode. This is for my convenience to make images for this explanation easily and telling difference between already decided area and current area under consideration.

Note the overlapping area in these two considerations. This area will be solid in either case. Therefore, it can be decided as solid area. Figure (d) shows the result of this trial.

The result is indicated in orange in this figure to show the result of this trial in the whole grid.

Now look at the clues of the third, fourth, and fifth rows. They are (1,1), (1,2,2,1), (1,1,1) respectively.

The leftmost blocks of these rows correspondent to their first clue, 1, as (1,1), (1,2,2,1), (1,1) respectively. Since these blocks already satisfy the conditions, they will have blank blocks next to them.

Those blocks are marked with orange for explanation.

I am surprised with myself explaining this puzzle step by step in detail. This explanation continues to next page. Some users who are already used to this puzzle may think this too much. But the popularity of puzzles are supported by beginners greatly, so I'm going to provide detailed knowhow to help them enjoy puzzles.

Continue to page 2 >>>

All rights reserved to Hirofumi Fujiwara for all the knowhow and contents of Key to solution for Nonogram page.