Akari (Light Up)

Place light bulbs in white cells so every cell is lit and no two bulbs shine on each other.

What it is

A grid of white and black cells. Some black cells carry a number: exactly that many bulbs must sit in the (up to four) white cells beside it. A bulb lights every cell in its row and column until a black cell blocks the beam. The goal: every white cell lit, and no bulb in another bulb’s beam.

How to play

Start at the numbers. A “4” forces bulbs on all four sides; a “0” forbids all four. A numbered cell whose remaining free neighbours exactly match its count forces them all. Cells that no candidate bulb can reach must themselves hold a bulb. Mark cells that cannot hold a bulb (lit cells, and neighbours of a satisfied number) — the answer falls out of the interaction.

Purpose

A gentle, visual entry into constraint puzzles — beams are easy to see, and the “no two bulbs see each other” rule reads instantly. In the workspace it is also the crate that showed a whole generator can work without search: placing bulbs greedily and lighting everything is a loop that cannot fail.

History

Introduced by Nikoli in 2001 as Bijutsukan (“art gallery”), published in English as Akari or Light Up. It descends from the mathematical art-gallery illumination problems, turned into a pencil puzzle with the beam-blocking twist.

This implementation

• Spec knobs: rows, cols, wall_share, numbered_share, difficulty.
• Generation: answer first — walls are scattered, bulbs are placed by a greedy pass that provably lights everything, numbers are read off the walls, and numbers are thinned while the board keeps exactly one answer.
• Guarantees: count_answers(2) == 1 over the walls and surviving numbers; every number re-checked against the bulbs actually beside it. The search was cross-checked against brute force over every wall pattern of a 3×3 and every bulb subset of each — 512 boards, no exceptions.
• A lesson recorded: a wall blocks a column as well as a row, and all four neighbours of a wall can hold bulbs — two “obvious” assumptions the brute-force sweep corrected during development.