Solve online here.
Rules: Standard Shikaku rules.
Divide the grid into rectangles such that each rectangle contains exactly one number and such that this number equals the area (i.e. the number of cells) of the rectangle.
Here is a grid of Shikaku and its solution.
Solve the example online here.
According to the WPC unofficial wiki, Shikaku is a puzzle first published in 1989 in Nikoli. It was invented by Yoshinao Anpuku.
Place some stars in the grid, no more than one by cell, such that the number of stars in each row, column and region equal the indicated number. Stars cannot share an edge or a corner.
Here is an example of a Star Battle grid and its solution.
Solve the example online here.
According to gmpuzzle, Star Battle was invented by Hans Eendebak from the Netherlands in 2003 for the World Puzzle Championship.