Number Logic Puzzles Rules

Sudoku

Sudoku is a logic-based, number-placement puzzle. The goal is to fill a grid with digits so that each column and each row contain the digits only once.

No Blocks (Latin Square)

Latin Square is an n x n array filled with n different digits, each occurring exactly once in each row and exactly once in each column.

Latin Squares Rule:
  • Each column and each row contain the digits only once.

Rectangular Blocks

The most common limit is the Rectangular Blocks. A 9x9 grid has 9 blocks, as seen in the picture.

Rectangular Blocks Rules:
  • Each column and each row contain the digits only once.
  • Every block contains each of the digits only once.

Irregular Blocks (Jigsaws)

Jigsaw puzzle is played the same as Sudoku, except that the grid has Irregular Blocks, also known as cages.

‭Irregular Blocks Rules:
  • Each column and each row contain the digits only once.
  • Every cage contains each of the digits only once.

Diagonal Variants

It is common to add limits on the placement of the digits, beyond the usual row and column. One of the limits is the Diagonal Variant.

Diagonal Variants Rule:
  • Every diagonal line contains each of the digits only once.!

Combined Variants

Variants can be combined. For example: the grid can have both Rectangular Blocks and Diagonal Lines. There can also be more than 2 diagonal lines.

Rectangular Blocks and Diagonal Variants Rules:
  • Each column and each row contain the digits only once.
  • Every block contains each of the digits only once.
  • Every diagonal line contains each of the digits only once.

Overlapping Variants

Overlapping variant consits of several puzzles. Shared blocks are highlighted by a different color. Here are some examples of overlapping Sudokus:

Double-Doku
Sensei
Gattai Near-2
Wing-3
Gattai-3
Sohei
Butterfly
Flower-4
Samurai
Gattai-8

Killer

The grid of the Killer Sudoku is covered by cages (groups of cells), marked with dotted outlines. Each cage encloses 2 or more cells. The top-left cell is labeled with a cage sum, which is the sum of all solution digits for the cells inside the cage.

Killer Sudoku Rules:
  • Each column and each row contain the digits only once.
  • All digits in a cage should be distinct.

Greater/Less Than

Greater Than (or Less Than) Sudoku has no given clues (digits). Instead, there are "Greater Than" (>) or "Less Than" (<) signs between adjacent cells, which signify that the digit in one cell should be greater than or less than another.

Greater Than / Less Than Rules:
  • The goal is to fill a grid with digits so that each column and each row contain the digits only once.
  • Digits must obey the inequality signs.

Kakuro

Kakuro is played on a grid of filled and barred cells, "black" and "white" respectively. The grid is divided into "entries" (lines of white cells) by the black cells. The black cells contain a slash from upper-left to lower-right and a number in one or both halves. These numbers are called "clues".

Kakuro Rule:
  • The goal is to insert digits from 1 to 9 inclusive into the white cells in such a way that the sum of the digits in each entry matches the clue associated with it and that no digit is duplicated in any entry.

Kenken

The grid is divided into heavily outlined cages (groups of cells). The numbers in the cells of each cage must produce a certain "target" number when combined using a specified mathematical operation (either addition, subtraction, multiplication or division).

Kenken Rules:
  • The goal is to fill a grid with digits so that each column and each row contain the digits only once.
  • Digits may be repeated within a cage as long as they are not in the same row or column.

Futoshiki

Futoshiki is played on a grid that may show some digits at the start. Additionally, there are "Greater Than" (>) or "Less Than" (<) signs between adjacent cells, which signify that the digit in one cell should be greater than or less than another.

Futoshiki Rules:
  • The goal is to fill a grid with digits so that each column and each row contain the digits only once.
  • Digits in adjacent cells with inequality signs must obey the greater than or less than signs.

Straights

Straights is played on a grid that is partially divided by black cells into compartments. Compartments must contain a straight - a set of consecutive numbers - but in any order (for example: 2-1-3-4). There can also be white clues in black cells.

Straights Rules:
  • Each column and each row contain the digits only once.
  • Each compartment, vertically or horizontally, must contain a straight.
  • Clues in black cells remove that digit from the row and column, and are not part of any straight.

Skyscraper

The Skyscraper puzzle has numbers along the edge of the grid. Those numbers indicate the number of buildings which you would see from that direction if there was a series of skyscrapers with heights equal the entries in that row or column. For example: if the line has 4 cells and if the first number in the cell is 4, you will see only one skyscraper because the 4-floor skyscraper hides the 1-floor, 2-floor, and 3-floor skyscrapers.

Skyscrapers Rules:
  • The goal is to fill in each cell with numbers from 1 to N, where N is the size of the puzzle's side.
  • Each column and each row contain the numbers only once.

Skyscrapers with Parks

The Skyscrapers puzzle can have Parks (empty cells).

Skyscrapers with Parks Rules:
  • The goal is to fill in each cell with numbers from 1 to N-(No. of Parks), where N is the size of the puzzle's side.
  • Each column and each row contain the numbers only once.

Sum Skyscrapers

The numbers along the edge of the Sum Skyscraper grid indicate the sum of heights of the visible buildings.

Sum Skyscrapers Rules:
  • The goal is to fill in each cell with numbers from 1 to N [or 1 to N-(No. of Parks) in Sum Skyscrapers with parks] where N is the size of the puzzle's side.
  • Each column and each row contain the numbers only once.

Binary

Complete the grid with zeros (0's) and ones (1's) until there are just as many zeros and ones in every row and every column.

Binary Rules:
  • No more than two of the same number can be next to or under each other.
  • Rows or columns with exactly the same content are not allowed.
  • When the line length has an odd number of cells, the number 1 exceeds the number 0.