Skyscrapers

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.

Rules

Here are the direct rules of the puzzle

1. Each row and column must contain the numbers 1-N, N being the width of the board.

2. 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.

LEGUP Proof Rules

Case Rules

Cell For Number

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.

Number For Cell

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.

Contradiction Rules

Duplicate Number

This can be easily derived from Rule #1. Use this when a number appears twice in a row or column

Unresolved Number

Comes from Rule #1. Use this when Cell For Number returns no cases. No possible cell for a number without a duplicate contradiction.

Unresolved Cell

Comes from Rule #1. Use this when Number For Cell returns no cases. Elimination leaves no possible number for a cell.

Too Few Visible

Derived from Rule #2. Use this when there are less skyscrapers visible in a row or column than there should be.

Too Many Visible

Derived from Rule #2. Use this when there are more skyscrapers visible in a row or column than there should be.

Preemptive Visibility

Derived Rule #2. Use this when the row/col isn't full yet, but a visibility contradiction is inevitable.

Direct Rules

N-Edge

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.

Last Non-Duplicate Cell

From Rule #1. Use this when there is only one Cell For Number that does not create a Duplicate Contradiction.

Last Non-Duplicate Number

From Rule #1. Use this when there is only one Number For Cell that does not create a Duplicate Contradiction.

Last Visible Cell

From Rule #2. Use this when there is only one Cell For Number that does not create a Preemptive Visibility Contradiction.

Last Visible Number

From Rule #2. Use this when there is only one Number For Cell that does not create a Preemptive Visibility Contradiction.