## A quicker way to find skyscrapers, 2-stringkites and x-wings

Advanced methods and approaches for solving Sudoku puzzles

### A quicker way to find skyscrapers, 2-stringkites and x-wings

As someone who prefers to delay the use of pencilmarks for as long as possible or not use them at all, I've tried to come up with a method that helps me determine when the moment has arrived to cave in and place them. This is usually when chains are required or when I've missed an XY-Wing or XYZ-wing in a grid with still a lot of unsolved cells. For some reason I have a very good memory for which candidates still remain, but when following a chain with more than 3 steps tend to lose track quickly! However, I don't like placing pencilmarks and then finding a pattern I should've and could've found without them!

My regular scanning usually catches pairs, triples and quads and a number of uniqueness based patterns and I'm usually pretty confident when these are no longer available. Lately I've also become better in spotting single digit patterns like x-wings, 2-string kites, skyscrapers and empty rectangles. To make sure these don't remain I make use of the following observation about these related and overlapping techniques: they involve four boxes forming a rectangular pattern.

For each number I try to find such patterns by eliminating boxes that cannot be part of it: boxes where the number has already been placed or where the remaining options for that number are aligned in the same row or column. When the remaining boxes can form the corners of a rectangle I check if they might containg one of the patterns mentioned above. Only when I'm confident they no longer exist I take out my pencil!

Anyone else here that 'hates' pencilmarks?
Ardnas

Posts: 3
Joined: 30 July 2008

Ardnas, Welcome to the Forum.

I believe that RW is the king of solving without pencilmarks and you can read his thoughts here
Bigtone53

Posts: 413
Joined: 19 September 2005

The Superior Thread (Second Collection) is dedicated to non-pencilmark solvers.

tarek

tarek

Posts: 2677
Joined: 05 January 2006

Thanks, I'll refer to those threads and post any additional thoughts there!
Ardnas

Posts: 3
Joined: 30 July 2008