---
name: Skyscraper
url: https://rules.sudoku-sleuth.com/skyscraper.md
kind: skyscraper
parameters:
  cells:
    description: The marked cells, for example r1c1-r1c2-r2c2.
    default: Required.
    type: list<cell>
  visible:
    description: The number of digits visible from the clue.
    default: Required.
    type: position
---

# Skyscraper

Read from the clue. A digit is visible when it is greater than every digit before it. The clue counts visible digits.

## Parameters

| Parameter | Meaning | Default |
| --- | --- | --- |
| cells | The marked cells, for example r1c1-r1c2-r2c2. | Required. |
| visible | The number of digits visible from the clue. | Required. |

## Maths

Class: **with aggregates**.

The [shared predicates](https://rules.sudoku-sleuth.com/predicates.md) define the notation and every named predicate.

```text
|{i∈[0,|cells|): ∀j∈[0,i): D(cells[j])<D(cells[i])}|=visible
```

visible equals the count of positions whose digit is strictly greater than all preceding digits, reading from the clue.

## Example

````markdown
---
format: open-rules
title: Skyscraper example
setter: Example
source: ""
case: ""
library: https://rules.sudoku-sleuth.com/
status: read
---

```rules
sudoku 9x9
skyscraper r1c1-r1c2-r1c3 visible 2
```
````

Satisfies the rule: r1c1=1, r1c2=3, r1c3=2. 1 then 3 are visible; the later 2 is hidden.

Breaks the rule: r1c1=1, r1c2=2, r1c3=3. All three increasing digits are visible, exceeding clue 2.