Battle Picross Tutorial
=======================

To solve a puzzle, you need to reveal the hidden picture in the 
playing board. You are given hints by the numbers in the rows and 
columns to the top and left of the playing board. The numbers 
represent blocks of consecutive squares.

Since the playing board is a size of 20x12 squares, the biggest 
possible block in a row is 20. Now, if there were two blocks of 
squares in a row, its number would show "11 8". However, this adds 
up to 19, not 20. This is because there must be at least one square 
that is not part of the picture. Otherwise, there would be a single 
block of 20 squares. So, when solving the puzzle, an X should be 
placed instead of chizzeled. Note: there is only one possible way to 
chizzel "11 8" in a row. With experience, you will find tricks which 
can be used to solve the puzzle without guessing.

Quick Walk-Through
==================

Here is a simple 5x5 puzzle spelling "Hi":

#   #   #
#   #  
# # #   #
#   #   #
#   #   #

The numbers for the puzzle would be as follows:

       |          1
       |  5 1 5 0 3
-------------------
1 1 1  |  #   #   #
  1 1  |  #   #
  3 1  |  # # #   #
1 1 1  |  #   #   #
1 1 1  |  #   #   #

Let's observe the colums of the puzzle.  This means that you will 
be concerned with looking at the numbers at the top of the screen.
the first column lists 5.  This means that there is a continuous 
block of 5 pixels in the puzzle.  You can see that this is the 
first vertical line of the "H" letter.  Since we know that the 
puzzle is a 5x5, there can only be one possible way that a block 
of 5 pixels can lie: the exact 5.  So, when starting a new puzzle 
look for these numbers.  Chizzel all the way down!

Now, look at the fourth column.  It lists 0.  This means that there 
are no pixels in that column.  You might as well mark the board 
off with "X"s because there are no blocks of continuous pixels in 
that column.  This is another cool tactic to use.

If you started this puzzle from scratch, it may look like this 
right now:

       |          1
       |  5 1 5 0 3
-------------------
1 1 1  |  #   # x   
  1 1  |  #   # x
  3 1  |  #   # x    
1 1 1  |  #   # x   
1 1 1  |  #   # x   

Alright, the puzzle is beginning to take form.  Look at the second 
row.  It lists 2 blocks of pixels, 1 each.  By chizzeling away at 
the obvious columns, we have automatically revealed the 2 blocks 
of 1 pixel groups.  Since you've revealed everything you needed on 
that row, you can mark the rest of that row with "X"s.  The puzzle 
should now look like this:

       |          1
       |  5 1 5 0 3
-------------------
1 1 1  |  #   # x   
  1 1  |  # x # x x
  3 1  |  #   # x    
1 1 1  |  #   # x   
1 1 1  |  #   # x   

Look at column 5 now.  There is an "X" marked away since we know that 
it isn't part of the picture.  Remember that this is a 5x5 puzzle, 
so this leaves 4 possible pixels.  But, you may have noticed that the 
remaining 4 pixels can fit 1 and 3 downward respectively.  Go ahead 
chizzel these in:

       |          1
       |  5 1 5 0 3
-------------------
1 1 1  |  #   # x #  
  1 1  |  # x # x x
  3 1  |  #   # x #  
1 1 1  |  #   # x # 
1 1 1  |  #   # x # 

There is one pixel left to chizzel (the crossbar in the letter "H").  
By the same rule as the previous paragraph, there is one way to allocate 
the block of 3 pixels.  Chizzel the pixel at 1 across, 3 down, and then 
you are done:

       |          1
       |  5 1 5 0 3
-------------------
1 1 1  |  #   # x #  
  1 1  |  # x # x x
  3 1  |  # # # x #  
1 1 1  |  #   # x # 
1 1 1  |  #   # x # 

Success, you win!  Notice that if you were playing Battle Picross, you 
didn't have to mark the entire board with "X"s.  This is because marking 
the board with "X"s is just to help you reveal the puzzle by eliminating 
tiles by process.

You may have also noticed another trick.  If you add up 1 + 3, it equals 
4.  However, if there are to blocks of pixels, they are separated with 
at least one non-picture pixel.  This makes 5.  So, the only way to reveal 
a row/column labeled as "1 3" is by chizzeling in this order: 1, blank, 3.  
Battle Picross uses 20x12 puzzles, so anthing that adds up to 20 horizontally 
or 12 vertically enables you to use this trick.

A more complex grouping could also be "3 5 2 3 3".  There must be at least 
4 non-picture pixels in order to break apart these groups of pixels.  But, 
add up all of the groups and blanks: 3 + 1 + 5 + 1 + 2 + 1 + 3 + 1 + 3 = 20!
Therefore, there was only one way to chizzel this line!  Go ahead, do it:

    ###x#####x##x###x###

Final Tip: Shifting Pixel Blocks
================================

Let's say that you had a 20x12 puzzle with a row of 18.  There is a small 
set of ways that 18 can be chizzeled.  In fact, here are the only three 
possibilities:

 1) ##################xx
 2) x##################x
 3) xx##################

What you may notice is that the center 16 pixels are always covered no 
matter what way the block of 18 lies.  So, you might as well chizzel those 
center 16!!  You don't have to mark the ends with "X"s, since you dont know
if the pixels appear on either end.  However, it may become revealed to 
you later on!

This shifting pixel block principle works with any size of pixel blocks 
of at least half the row size plus 1.  So, a row listing "16" would allow 
you to chizzel the center 12 pixels without risk, leaving 4 tiles on either 
end.

There are more tricks to puzzle solving, but can you find them out on your 
own?  Play and you might find more!

Good Luck!
