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Skyscraper in sudoku

A Skyscraper is about one number in two rows (or two columns). In each row the number can go in only two cells. One cell of each row lies in the same column: that is the base. The two other cells are the tops, and they stand in different columns, like two towers of unequal height. Every cell that shares a row, column or box with both tops loses the number.

Difficulty
Extreme

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How to spot it

Pick a number and find the lines where it is noted in exactly two cells. Look for two parallel lines with one end in a common cross line. Then find the cells that see both remaining ends: they are usually in the boxes of the two tops.

Why it works

The base column can hold the number only once, so at most one of the two base cells has it. The row whose base cell does not have it must have the number in its top. So at least one top holds the number, and a cell that sees both tops cannot.

On a real puzzle

This is Skyscraper on its practice puzzle, at the first step that needs it. The game's hint explains the step like this:

Skyscraper
  1. Look at the highlighted cells.
  2. Look at their notes: whichever way they are filled, the same notes are ruled out.
  3. So 7 can be removed from the crossed-out cells.

Practice it

This Extreme puzzle calls for Skyscraper. Fill in the singles first. When no number is obvious any more, look for the pattern, or ask for the hint: each game has one.

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