Shakashaka

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An eight-by-eight Shakashaka puzzle grid. Some of the spaces are pre-filled with black squares (some of which contain numbers); others are blank spaces to be filled with triangles.
An example Shakashaka puzzle
The solution to the previous puzzle.
The same puzzle with solution marked in teal

Shakashaka (シャカシャカ) is a logic puzzle developed by publisher Nikoli.[1] The objective is to fill the white squares in a given grid with a pattern of triangles such that each white area in the resulting grid has a rectangular shape. Furthermore, each black square in the grid marked with a number must be orthogonally adjacent to the specified number of triangles.[2]

Computational complexity[edit]

It is NP-complete to decide whether a given Shakashaka puzzle has a solution.[3] Furthermore, counting the number of solutions to a given Shakashaka puzzle is #P-complete.[3]

References[edit]

  1. ^ "Puzzles of nikoli.com". Nikoli. Retrieved 14 August 2014. 
  2. ^ "Rules of Shakashaka puzzle". Nikoli. Retrieved 14 August 2014. 
  3. ^ a b Demaine, Erik D.; Okamoto, Yoshio; Uehara, Ryuhei; Uno, Yushi (2014), "Computational complexity and an integer programming model of Shakashaka", IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E97-A (6): 1213–1219