# How to beat “Strata”?

Recently I purchased a bunch of mobile puzzle games for my iPhone and one of them was the famous top-rated app "Strata" by Graveck. The rules are simple - you begin with an $n \times n$ board, some squares of which are colored in arbitrary colors. Then you start placing stripes of whatever color you choose over entire rows and columns of the board. Your task is after placing all available $2n$ stripes, the color of every (colored) square to match the color of the stripe which has been placed second over it (on top).

Can you find an easy way to beat every single level of this game?

P.S. You can see a video explanation of the rules in the app review below: https://www.youtube.com/watch?v=NwjyOpA14Vk

• Is every puzzle guaranteed to have a unique solution? – 2012rcampion Oct 21 '15 at 4:50
• It is possible that a level has multiple solutions (at least one). – Puzzle Prime Oct 21 '15 at 6:42
• @2012: Actually, no puzzle can have a unique solution. You can always whittle it down to have all uncovered squares left on the board (even if it's just 1) the same color, and then you can do rows first or columns first. – Deusovi Oct 21 '15 at 14:22

Here's a foolproof way to do it:

Fill in any "consistent" rows and columns first - anything that has all the same color (or gray).

Ignore those squares and fill in newly consistent rows and columns. There will only be none if the puzzle is unsolvable.

Once you're done, reset and do the entire thing in reverse order.

• I don't think this works as described. Consider the square {{1,1},{2,3}}. If you first fill in the consistent {1,1} row, that will take two strips. There will then not be enough strips left to fill the {2,3} row. – Taemyr Oct 21 '15 at 12:40
• @Taemyr: How does it take two strips? You just use a strip on the top row, then get one of the consistent columns, then finish off the last tile. – Deusovi Oct 21 '15 at 13:02
• Right. You have to finish the top row last. Your answer implies finishing it first. – Taemyr Oct 21 '15 at 13:04
• @Taemyr: Read the last line. It says reset and do the entire thing in reverse order. – Deusovi Oct 21 '15 at 13:45
• That's right. If you can give a little bit more details why the puzzle will be unsolvable if you can't apply this procedure would be great though. Still getting the "correct answer" anyway. – Puzzle Prime Oct 21 '15 at 16:59

Not sure if it always lead to solutions but I think that this strategy is pretty solid for the easier levels at least:
Always do the columns or rows in order of most colors to least colors in that row or column.

To explain it further. If a row or column has only a single color do that one last. It's kinda logical in a way because if you didn't do it last there is a possibility that a square is overwritten in another direction later on. And it's then also impossible for that last move to screw up other squares.

This automatically means that rows that have more colors come first. And the more colors you have the more you need to overwrite colors in that row or column so more colored rows have priority over rows with less colors.