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This is a 5x5 grid. Look at the numbers next to the rows and columns. They tell you how many filled squares there will be in that line. Solve the highlighted row first, by selecting the squares you know are filled and tapping the Hand tool.
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Notice that the 5 next to that row is gone now; the numbers for solved lines disappear. Now let's solve the 5 column. It should be easy too.
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The 4 means that there are 4 squares filled, without any gaps. Because the 1st square is filled, remaining 3 must be next to it. That means the last square in the row is blank!
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Use the same logic to solve highlighted column.
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Can you handle this one on your own? There's only one filled square left to find; figure out which it is, and solve it!
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Deleting empty squares will make solving puzzles easier! Select the squares you know to be empty and use the Hammer tool to delete them.
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When there's more than one number, the groups of filled squares must be divided by gaps of at least one empty square. So here, 3 1 means that there are 3 filled squares, a gap, and 1 more filled square.
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Just like last time, 2 2 means that there are 2 filled squares, then a gap, then 2 more filled squares. On a 5x5 grid, it's pretty easy to figure out where they have to go!
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The easiest lines to solve are the ones where the sum of the filled squares and mandatory gaps is equal to the grid size. For instance, in the last row, you know there must be three filled squares and two gaps, so there's only one possibility.
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These rows are empty. Let's clear them to make solving the rest of the puzzle easier.
A bit of a challenge
Uh oh! Now we have 3 filled squares and 2 empty ones. This gives us 3 possibilities, as shown in the animation. But notice that in all these possibilities, there's one square that's always filled; mark that one as solved!
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Great! Let's take a look at another row.
There's no need to guess! 
Let's take a look at another row. Again, we have 3 possibilities, and again one square is always filled. Mark that one as solved.
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You should already know how to solve this one.
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We know that the highlighted squares are filled, because there is only one valid combination.
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Now it's easy to solve this row. There's only one combination and it's highlighted. Solve the filled squares.
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Let's clear the last square in this row, because we know it's empty.
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This column has just one full square, and the rest can be broken.
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Solve the remaining squares in the 3rd row.
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Break the empty squares in the 4th column.
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Solve the last square to finish this puzzle!
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Breaking tiles
To break empty tiles you need to use the Hammer tool.
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Solving easy rows or columns should be your first priority. It makes solving the other ones much easier.
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Each number is a clue. It indicates how many of the surrounding squares, including the numbered square itself, must be filled with the corresponding color. A 9 is easy - the whole 3x3 area around the number must be filled.
A 4 in a corner and 6 on the edge are just as easy. There's only one correct solution!
A 0 tells you that it and all surrounding squares are empty.Those tiles are automatically crossed out for you.
Solve the 6 first. 
The numbered squares themselves can be empty or filled with their own color, but never with another color. Use that fact to help you solve this one.
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Solve the 9 first. 
You need to switch to the other color now. When you change colors, tiles and hints of the other colors are faded out. Change the tile color to white and solve the 8.
As you can see, both 2s are already completed. The rest of the surrounding tiles must be empty, so cross them out by selecting X from the color palette. This will help you solve the 1. 
Each level has only one solution which fits all the clues. If you correctly solve the clues then you will never need to to guess.