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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.

Some info about Light Up/Akari:

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:


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

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

Yay, the first puzzle!

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    $\begingroup$ 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. $\endgroup$ Feb 27 at 18:44
  • $\begingroup$ @GentlePurpleRain I could edit it to include that info, yes $\endgroup$
    – CrSb0001
    Feb 27 at 18:45
  • $\begingroup$ If the puzzle has enough empty squares, the Akari rule is ambiguous: it isn't clear if a bulb is allowed to illuminate itself. $\endgroup$
    – Bubbler
    Feb 28 at 7:29
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    $\begingroup$ Penpa+ link: tinyurl.com/2d9pggfz Select composite tab to insert light bulbs. $\endgroup$
    – ACB
    Feb 28 at 10:08

1 Answer 1

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I believe this works:

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Each yellow square in the grid is a lamp, labeled a through n. The solution was actually surprisingly straightforward, there need to be four lamps surrounding the black square in H3, and from there everything followed naturally - at each stage there was another black square whose lamps had only one possible placement. See the following images for a step by step solution:

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