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Griddlers Tutorial - Solving Puzzles

Example 1: A Simple Puzzle
Example 2: A Triangle Puzzle
Example 3: Multi Line Solving
Example 4: Complex Logic (a)
Example 5: Complex Logic (b)
Example 6: Color Elimination
Example 7: Complex Color Logic
Example 8: More Color Logic


Example 3: Multi Line Solving

Here's an example of MLS (Multi Line Solving).
This type of logic involves looking at clues in more than one row or column at a time.
Look at the last row. If we can figure out where to put the group of 10 it would be a big help to us.

First, look at what happens when you color the last 10 squares in black and fill in the resulting columns. Since the clues for the 19th row are 1,1, the row clues are violated (marked with red dots). The 10 cannot be in this position.
In fact, you can see that any group of 10 that involves the 13th square (marked with green arrow) is impossible since this would also have to include the 12th square and thus create a group of "2" (encircled with red) which contradicts the clues "1" in the 19th row.
Therefore, we can color in white the 13th square (marked with a red dot) and also any square to the right of it. Now we have a group of 8 we can confidently color in black.
We can also look at the clue 8 in the last column (marked with a red arrow). We must have a group of 8 black. But we know that we can only have a group of 2 squares maximum colored in the 19th column (circled in red). As you can see, this eliminates the first 6 squares in the column.
The black square marked with X has to be white too.
Let's try to place the group of 8 at the bottom. Using the same logic, the black squares marked with X have to be white also.
Once we color those in white we can easily color in a group of 7 blacks. This would be our result. You can see that just by using simple MLS we can get a big jump start on this puzzle.
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