## Sudoku-esque puzzles with Latin roots

For fans of all other kinds of logic puzzles

### Sudoku-esque puzzles with Latin roots

The variations posted in this previous thread are (for the most part) direct descendents of Sudoku, which in turn is a direct descendant of Latin Squares. They are Sudokus children. On the other hand, the puzzles in this post are direct descendents of Latin squares -- sisters to Sudoku.

Like Sudoku, the published versions you might come across are probably no where near as hard as it is possible to make them. Because the idea is to fill cells with digits, the same type of pencil-marking can be used. Programmers shouldn't face too many challenges in adapting their existing software to create/solve these.

SKYSCRAPER puzzles aka FLATS, APARTMENTS, etc, are a very close sister to Sudoku. The solution array is a latin square. There is no reason that additional constraints couldn't be added -- a 9x9 Skyscraper puzzle that required one of each digit in each 3x3 box *would* be a Sudoku variant, and could be solved using many of the same candidate reduction tactics.

===============================================
SKYSCRAPERS
Fill the grid with the digits 1 to N, where N is the length of the side of the puzzle. The digits represent the height of the Skyscraper in each cell. Each row and column will have exactly one of each digit. The clues along the egdes tell you how many Skyscrapers you can see from that vantage point. For example, if you look down the row at this -- 13254 -- you'll "see" the 1, the 3 and the 5. The 2 will be hidden behind the taller 3, the 4 will be hidden behind the taller 5.

5X5 Skyscraper
Code: Select all
`    3 2 1 3 2  +-----------+2 | . . . . . | 2 2 | . . . . . | 32 | . . . . . | 21 | . . . . . | 34 | . . . . . | 1  +-----------+    2 3 2 2 1 `

Solution:
Code: Select all
`    3 2 1 3 2  +-----------+2 | 3 1 5 2 4 | 22 | 2 5 3 4 1 | 32 | 4 3 1 5 2 | 21 | 5 4 2 1 3 | 34 | 1 2 4 3 5 | 1  +-----------+    2 3 2 2 1 `

6x6 Skyscraper
Code: Select all
`    1 3 2 2 2 4  +-------------+1 | . . . . . . | 5  3 | . . . . . . | 34 | . . . . . . | 22 | . . . . . . | 22 | . . . . . . | 35 | . . . . . . | 1  +-------------+    4 2 4 3 2 1`

7X7 Skyscraper
Code: Select all
`    1 2 5 6 4 2 3  +---------------+1 | . . . . . . . | 4  2 | . . . . . . . | 2 5 | . . . . . . . | 22 | . . . . . . . | 23 | . . . . . . . | 54 | . . . . . . . | 14 | . . . . . . . | 3  +---------------+    4 2 2 1 4 3 2 `

===============================================
GREATER THAN/LESS THAN
Object is to form a simple latin square. Clues are greater than and less than signs between cells. (I'm using V and Λ as vertical versions of < and >.) Sometimes these puzzles will also have equal signs and/or only have signs between some of the cells. Again, this could easily be done with a 9x9 array including the additional 3x3 boxes of standard Sudoku.

Code: Select all
`[ ]>[ ]<[ ]<[7]>[ ]>[ ]<[ ] V   Λ   Λ   V   V   Λ   V [2]<[ ]>[ ]<[ ]>[3]<[ ]>[ ] Λ   Λ   V   V   Λ   V   Λ [ ]<[ ]>[1]<[ ]>[ ]<[6]>[ ] Λ   V   Λ   V   Λ   V   Λ [ ]>[ ]<[ ]>[ ]<[ ]>[ ]<[5] V   Λ   V   Λ   Λ   Λ   Λ [ ]<[3]>[ ]<[4]<[ ]>[ ]<[ ] Λ   Λ   Λ   V   V   V   V [ ]>[ ]>[ ]>[ ]> 1 <[ ]>[ ] V   V   Λ   Λ   Λ   V   Λ [ ]>[4]<[ ]>[ ]>[ ]>[ ]<[7]`

===============================================
EASY AS ABC(DE) aka LETTERRAAM. is not quite as close a sibling -- maybe more of a cousin of Sudoku. Their solution arrays are not quite latin squares, as they include one or more spaces. Puzzles with more than one space per row/column are generally more difficult.

EASY AS ABC(DE) aka LETTERRAAM.
Each row an column of the solution contain exactly one of each letter plus one or more spaces. The clues around the perimeter tell you which letter appears first in that row or column.

Standard type. Clues show FIRST solution letter in the row or column.

4X4, ABC
Code: Select all
`    C   A      +---------+  | . . . . |  | . . . . |C | . . . . |  | . . . . |  +---------+          B  `

Solution:
Code: Select all
`    C   A      +---------+  | C B A . |  | B A . C |C | . C B A |  | A . C B |  +---------+          B  `

5X5, ABCD
Code: Select all
`    B A  +-----------+  | . . . . . | CD | . . . . . |   | . . . . . |   | . . . . . |   | . . . . . | D  +-----------+    B       B`

5X5, ABC
Code: Select all
`      B   B  +-----------+  | . . . . . |    | . . . . . |   | . . . . . | A  | . . . . . |   | . . . . . | B  +-----------+          C C`

6X6, ABCDE
Code: Select all
`      B E   D      +-------------+  | . . . . . . | E    | . . . . . . | B  D | . . . . . . | E    | . . . . . . |    | . . . . . . |    | . . . . . . |    +-------------+    C   A   A`

6X6, ABCD
Code: Select all
`      D   C   B            +-------------+B | . . . . . . |  C | . . . . . . |  B | . . . . . . |    | . . . . . . | A   | . . . . . . | D    | . . . . . . |    +-------------+    D B     B A`

7X7, ABCDEF
Code: Select all
`      D D   E A F  +---------------+  | . . . . . . . |  B | . . . . . . . | A  C | . . . . . . . |    | . . . . . . . | D A | . . . . . . . | E E | . . . . . . . | C   | . . . . . . . |    +---------------+        F B D E`

7X7, ABCDE
Code: Select all
`    A   E  +---------------+B | . . . . . . . | C  E | . . . . . . . | B    | . . . . . . . |    | . . . . . . . | C B | . . . . . . . |    | . . . . . . . | B    | . . . . . . . |    +---------------+    D D A   D C`

===========================================
In this variation, the clues tell you the SECOND letter you will see from that vantage point down that row or column.

6X6, ABCD, SECOND version
Code: Select all
`      D A D C B   +-------------+B | . . . . . . | A  D | . . . . . . |  A | . . . . . . | B   | . . . . . . | BC | . . . . . . | B   | . . . . . . | C  +-------------+      C C A   C `

===========================================
And finally, the mixed version. The clues tell you the first OR second letter you will come to. (So a "C2" means the second letter will be a "C".)

6X6, ABCD, MIXED version
Code: Select all
`     B A B   A B      2 2 2   2 2   +-------------+ B2| . . . . . . |D2   D2| . . . . . . |A2   | . . . . . . |C1    | . . . . . . | C2| . . . . . . |B2    | . . . . . . |A1   +-------------+     A   D   C D     2   2   2 2`
tso

Posts: 798
Joined: 22 June 2005

tso: do you have any refferences to a web-site having a number of Skyscrapers puzzles?
giant

Posts: 18
Joined: 09 August 2005

### Re: Sudoku-esque puzzles with Latin roots

tso wrote:They are Sudokus children. On the other hand, the puzzles in this post are direct descendents of Latin squares -- sisters to Sudoku.

What, no brothers?

I like the skyscrapers .... the property reminds me of something about permutations called an "inversion".

I wonder which sequences of numbers around the borders are possible.

Put another way, what is the total number of nxn skyscrapers?
Moschopulus

Posts: 256
Joined: 16 July 2005

Angela und Otto Janko's Home Page has 50 or 60 in 5 sizes.
tso

Posts: 798
Joined: 22 June 2005

On the PQRST puzzle site I found quite nice puzzle called there Eminent Domain. Does anyone know some other sites where I could find more of this particular kind of puzzles (somewhere i found a German name of this puzzle: Bereichsteilung). I will appreciate any information. Thanks.
giant

Posts: 18
Joined: 09 August 2005