A Skyscraper is a simple pattern that occurs rather often in sudokus and can be easily spotted. It is nothing really new: A Skyscraper is a special form of Turbot Fish and it can be seen as two Sashimi X-Wings .
The description of the pattern sounds more complicated than it really is: Concentrate on one digit. Find two rows (or columns) that contain only two candidates for that digit. If two of those candidates are in the same column (or row), one of the other two candidates must be true. All candidates that see both of those cells can therefore be eliminated. Let's look at examples:
Take the left example: In column 6 digit 1 can only be placed in row 1 or row 5. In column 9 digit 1 can only be placed in row 3 or row 5. r5c6 and r5c9 are in the same row (the "base" of the skyscraper). We can now reason as follows: If r1c6 is not true, then r5c6 must be true (only two possible values, one of them must be true:
). But if r5c6 is true, r5c9 cannot be true since they are in the same row (
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). And if r5c9 is not true, r3c9 has to be true ( air jordan release december 2017 weather
). We have thus proved, that r3c9 has to be true, if r1c6 is not true. The same argument holds if we start with r3c9 not true: It follows, that r1c6 has to be true. Since one of r1c6 and r3c9 has to be true, all candidates that can see both cells can be eliminated (in our example: r1c78 and r3c45).
Luckily for you it is not necessary to follow through the logic everytime you look for a Skyscraper: You only have to identify the pattern.
It can be seen, that the places of the candidates are subject to a restriction: The two top cells have to be in the same band or nothing can be eliminated.
The example on the right shows a Skyscraper, that has been rotated 90 degrees clock wise: Skyscraper on 4 in r2c5,r8c4 (connected by r28c1) => r1c4<>4
If we look at the left example again we can easily identify the two Sashimi X-Wings that are contained in it: The first is c59/r35, fin in r1c6, eliminating 1 from r3c45. The second is c59/r15, fin in r3c9, eliminating 1 from r1c78.
A 2-String Kite is a second special form of Turbot Fish , that can be found in lots of sudokus. The description: Concentrate again on one digit. Find a row and a column that have only two candidates left (the "strings"). One candidate from the row and one candidate from the column have to be in the same block. The candidate that sees the two other cells can be eliminated.
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