# Light Up (Akari), but on a real projective plane!

This is a Light Up (aka Akari) puzzle, except it is on what is called a real projective plane. A real projective plane is, simply put, just a Möbius strip with a single edge except for the fact that the opposite open edges are also glued together. This is different from a Klein Bottle because a Klein Bottle is a Möbius strip glued into a cylinder.

Light Up (Japanese: 美術館 bijutsukan, art gallery) which is also known as Akari (明かり akari, light) is a logic puzzle published by Nikoli in which players must place bulbs on a black and white rectangular grid such that no two bulbs shine light on each other.

A number on a square tells you how many bulbs surround the square orthogonally.

The goal is to eventually fill up the grid with light.

The puzzle:

Here is a coordinate system that I came up with if it would be helpful to reference it:

I can confirm that the solution to this puzzle is in fact unique.

Yay, the first puzzle!

• Could you explain the "real projective plane" criteria in non-mathematical language? How does it affect the puzzle. What is different from a typical Akari puzzle? Your description of the "real projective plane" does not make sense to me, nor does it tell me how it changes the puzzle's rules. Commented Feb 27 at 18:44
• @GentlePurpleRain I could edit it to include that info, yes Commented Feb 27 at 18:45
• If the puzzle has enough empty squares, the Akari rule is ambiguous: it isn't clear if a bulb is allowed to illuminate itself. Commented Feb 28 at 7:29
• Penpa+ link: tinyurl.com/2d9pggfz Select composite tab to insert light bulbs.
– ACB
Commented Feb 28 at 10:08