Another puzzle that challenged our users is described here:
Using simple logic we can fill in only this much.
Let's look at the square circled in green.
Looking at the column clues, we know that this could either be clue 1 or part of clue 7. Again, let's look at both possibilities.
Here's what the puzzle would look like if the square is clue 1.
Here's what the puzzle would look like if the square is the beginning of clue 7.
You can see that either way the square marked with a red dot must be white.