Rules: Divide the grid into rectangles such that each rectangle contains exactly one given number that represents the area of the rectangle in unit cells. Each cell in the grid must be part of a rectangle. The given numbers are replaced by their encoding letters; each different letter represents a different number.
Theme: Conjoined Twins
Rules: Shade in some cells such that shaded cells form all the Pentomino shapes without repetition, and with rotation and reflection allowed. Shapes cannot be edge-adjacent to one another. In the end, all unpainted cells must be connected in a single group through other unpainted cells.
Theme: Designated Parking
Rules: Locate some rectangular blocks in the grid, either 1 x 2 or 1 x 3 in size. Each given number should be a part of exactly one block, indicating in unit cells, the distance the block can possibly move. Blocks can only move into empty cells, and only in the direction perpendicular to their shorter edge. Each block has to have at least one block sharing an edge with it.
Theme: The missing prime
Rules: Shade in some cells to leave behind a single connected group of shaded cells, with no enclosed, shaded cells. In other words, all unshaded cells must be connected through other unshaded cells to an edge of the grid. All numbered cells must be a part of the cave, with each number indicating the total count of cells connected vertically and horizontally to the numbered cell, including the cell itself.
Theme: Relying on numbers
Rules: Place a number from 1 to N into each cell of the square grid so that each number appears exactly once in each row and column, where N is the length of the square's side. In this variant, the clues inside the cages are removed, and the new clues indicate the result of one of the four arithmetic operations (+,-,x,/) applied to the results of the operations inside the first two cages encountered when looking in the direction of the clue. Results are always integral. When an operator accompanies a given, it means that operator has to be applied.
About : This variant of TomTom is due to Anurag Sahay.
Theme: No operators
Rules: Place a number from 1 to N into each cell of the square grid so that each number appears exactly once in each row and column, where N is the length of the square's side. Each number inside the grid represents a skyscraper of its respective height. In the classic Skyscrapers puzzle, the outside clues would indicate how many skyscrapers are visible in that direction, with smaller skyscrapers hidden behind taller ones. In this variant, the regular clues are removed, and the new clues now indicate the result of one of the four arithmetic operations (+,-,x,/) applied to the regular skyscrapers clues in that row/column. Results are always integral. Operations may be provided as givens beside the result.
About : This variant of Skyscrapers was first proposed by Anurag Sahay.
Theme: Zeroed in on Zero
Rules: Locate the standard fleet of 10 ships into the given grid. Clues outside tell that many ship segments of a particular kind (of a total of three kinds as seen in the illustration) are in that direction. Segments of the other kinds must be in a quantity different from the clue, zero included. Ships may be rotated, but may not touch each other, not even diagonally. Cells with wave symbol are water, and do not contain ships.
Rules: Shade some cells so that all shaded cells are connected and no 2×2 square is completely shaded. Cells with numbers cannot be shaded. Each group of connected unshaded cells forms an island; islands can touch each other diagonally. Each island must contain exactly one given number, and that number indicates the sum of areas of ALL of the islands that touch (diagonally) the island it belongs to.
Theme: Bridging the Unknowns
Rules: Divide the grid into some Pentomino shapes along the grid lines. The shapes may be used more than once, with rotations and reflections allowed. Identical shapes may not touch each other through the edges. Letters indicate that the corresponding cells are used by the shapes the letters usually represent. Also, each shape using circled cells has to connect to an identical shape through one or more bridges. Two shapes are said to be connected if they are both edge-adjacent to the same shape.
Theme: 7 and 11
Rules: Divide the grid into some contiguous regions. Each cell is part of one region, and each region should contain exactly two given numbers, one in white circle and the other in shaded circle. Each region must have an area that is strictly between those two numbers.