Now, let's see how much you can solve a puzzle using rules in this section.
For this practice, I am using puzzle No1. This is an easy one (level **).


First you can use the "Rule of adjacent 3 and 0" here.


Next you can use the "Rule of adjacent 3 and 3" as this figure.


Now take a look at the puzzle and check if there is any place you can draw a line or mark with "x".


The "1" at the upper right of the adjacent "3 and 0" in the middle of the puzzle can be considered as "corner 1", so its left and bottom edges are marked with "x". Since there is "0" next to that "1", you cannot draw a line on the right edge, either. Therefore, you must draw a line on the top edge of "1". This line can be extended only upward as in this figure.
There is "1" at the left of adjacent "3 and 3" placed at lower right of this puzzle. Since it already has a line on the right edge, it is clear to mark "x" on all other edges.
Look at "2" on top of the "1". The bottom edge, sharing with "1", is already marked with "x". Also note there is "0" at its left. Obviously you cannot draw a line on the left edge, either. So you can draw two lines on remaining two edges.
Now remember the "Rule of adjacent 3 and 3". There are only two patterns to draw lines around them (Sshape or reversed Sshape). So you can automatically draw lines there, extending the end of line downward and to the left along the outmost edges of the puzzle.
Now use the "Rule of diagonal 3 and 3".


Let's think about how you can decide where to draw lines or put "x" on edges around that "diagonal 3 and 3".


The lines of diagonal 3 and 3 had to take a turn at blocked corners made by 0, connecting vertically at the sharing point of those 3 and 3.
There is only one edge left to draw a line for the "2" on top of the upper left "3" of the "diagonal 3 and 3".
The line, which comes into a vertex marked with star, must go upward. And since other two ways are blocked, it must take a right turn.
There is another "2". The left and bottom edges are already marked with "x" for the last "2", so you can extend lines along remaining edges.
The line will meet the blocked corner and again it takes right turn around "3", continues to extend around the edge of "3" and goes upward along the right edge.
You can apply the "Rule of corner 3" at these vertices (maked with stars).


After applying the rule, other places will be automatically decided as follonwing figure:


You can apply the "Rule of corner 2" as following figure:


Take a look at the lower left corner of this puzzle. The two lines drawn around "2" will go through those two vertices marked with stars. Since the right edge is marked with "x", the line will have to go through the corner vertex as shown in the figure.
Then the line will be connected with the line of above "3 and 3", deciding the rest of lines for the "3 and 3".
Now look at "2" at the lower right of this "3 and 3". Since you cannot draw lines at top and left edges, the remaining two edges will have lines.


The line extended along the bottom edge from the lower right corner of the puzzle connects with the line around "3" as this figure.
Then it decides the third line of that "3". The end of line will be extended upwards from the right edge of "adjacent 3 and 3".


Look at "3" on the left edge of the puzzle. One of its vertices (marked with a star) is blocked. So the "Rule of corner 3" is applicable here.
Now look at "2" placed at a little far right of the "3". Its bottom edge is already has a line because of the "3" placed at its bottom, and there is only one edge left to draw a line for this "2" (top edge). Since the top right vertex of this "2" is blocked, the line extends upwards, connecting with the line of "diagonal 3 and 3".
You can apply the "Rule of corner 2" for the "2" at the rightmost edge of the puzzle.


There are two possibilities for the corner 2, but since the other possibility makes dead end, you can draw lines this way.


And it decides where to draw lines around "3" on top of the "2". The line can be extended as this figure.
Actually there are some other places easily decided, but you need to read more rules to find them.
This is good for Practice 1 and I will stop for now.