Skyscrapers Rules
Skyscrapers is a puzzle with unfilled squares shown in gray. Your task is to fill all the squares with numbers without breaking the rules of the game.
Clicking on a tile increases the number in the square by 1, up to the width of the board.
Clicking on a tile of max height returns it to blank.
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Each row and column must contain the numbers 1-N, N being the width of the board.
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The numbers outside the board indicate the number of buildings visible from that perspective in that row or column. A larger number indicates a taller building, and taller buildings obscure the smaller buildings behind them.
Use this rule to create a branch in the proof for each possible location of the given number along the given row of column. Does not branch into cases that create a duplicate contradiction.
Use this rule to create a branch in the proof for each possible value of the given cell. Does not branch into cases that create a duplicate contradiction.
This can be easily derived from Rule #1. Use this when a number appears twice in a row or column
Comes from Rule #1. Use this when Cell For Number returns no cases. No possible cell for a number without a duplicate contradiction.
Comes from Rule #1. Use this when Number For Cell returns no cases. Elimination leaves no possible number for a cell.
Derived from Rule #2. Use this when there are less skyscrapers visible in a row or column than there should be.
Derived from Rule #2. Use this when there are more skyscrapers visible in a row or column than there should be.
Derived Rule #2. Use this when the row/col isn't full yet, but a visibility contradiction is inevitable.
A combination of Rules #1 and #2. Use this when N, the width of the board, appears as a clue. The numbers must appear in order increasing away from that clue.
From Rule #1. Use this when there is only one Cell For Number that does not create a Duplicate Contradiction.
From Rule #1. Use this when there is only one Number For Cell that does not create a Duplicate Contradiction.
From Rule #2. Use this when there is only one Cell For Number that does not create a Preemptive Visibility Contradiction.
From Rule #2. Use this when there is only one Number For Cell that does not create a Preemptive Visibility Contradiction.