Akari
Akari is a logic puzzle invented by あさおきたん (Asaokitan) and first published in Nikoli volume 95 (2001) under the original Japanese title 美術館 (Bijutsukan), meaning “Art Museum.” The name is likely a reference to the art gallery problem in computational geometry, which concerns how to place guards to observe an entire gallery.
In the puzzle’s metaphor, the grid represents a museum: numbered cells act as pillars, and other cells may hold light sources (originally imagined as guards). Each empty cell must be illuminated by at least one lamp, while no two lamps may shine on each other directly. When Nikoli prepared the puzzle for international publication, it introduced the English name “Light Up” and the Japanese title Akari (あかり), meaning “light.”
Beyond its thematic charm, Akari is also of theoretical interest — the decision problem “Is a given Akari puzzle solvable?” has been proven NP-complete (Brandon McPhail, 1985). Despite this computational complexity, most hand-crafted Akari puzzles are elegantly solvable through pure logic, contributing to its lasting popularity in Nikoli’s catalog and worldwide.
In the puzzle’s metaphor, the grid represents a museum: numbered cells act as pillars, and other cells may hold light sources (originally imagined as guards). Each empty cell must be illuminated by at least one lamp, while no two lamps may shine on each other directly. When Nikoli prepared the puzzle for international publication, it introduced the English name “Light Up” and the Japanese title Akari (あかり), meaning “light.”
Beyond its thematic charm, Akari is also of theoretical interest — the decision problem “Is a given Akari puzzle solvable?” has been proven NP-complete (Brandon McPhail, 1985). Despite this computational complexity, most hand-crafted Akari puzzles are elegantly solvable through pure logic, contributing to its lasting popularity in Nikoli’s catalog and worldwide.
Rules
Place light bulbs in selected white cells so that each white cell is illuminated. Light bulbs illuminate every white cell in all four orthogonal directions until blocked by a black cell. No light bulb can be illuminated by another light bulb. Clue numbers correspond to the number of light bulbs in the four orthogonally adjacent cells.
Click to see the answer.