## Puzzle 178 (Akari EX)

This is a Sunday Akari EX puzzle.

Puzzle 178

According to the about page, “sundays will be anything from hard to ridiculous; the only limit is that there is a logical solution with minimal thinking ahead.” Well, this one has a logical solution… but it takes the word ridiculous and goes to the sun with it, maybe to the point of being unreasonably hard. Puzzle 100, the 100 by 100 Akari, is a cakewalk in comparison.

Best of luck to anyone brave enough to tackle this one. And don’t worry, there won’t be another puzzle at this level for a long time, if ever.

1/31 4:11pm ET: Fix made to top right to eliminate a trivial ambiguity. Also, if you need a hint, feel free to check some of the comments.

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### 6 Responses to “Puzzle 178 (Akari EX)”

1. yy Says:

What happens if you switch C30R2 and C32R2 in the solution?

Adding a green 1 or 2 to the block at C33R3 is the only way to distinguish between the two options without changing other numbers in the puzzle or the solution.

Alternatively, changing the yellow 0 at C32R4 into a green 2 or 3 can distinguish between the two options, but I believe both of of these options allow additional solutions, in ways which I don’t think can be easily fixed.

2. MellowMelon Says:

Oops, point taken, the mirrors were all changed to diamond shapes late in production so that one slipped by me. If you solved it (sounds like you did), congratulations.

3. yy Says:

I did. The key to starting the puzzle is the 4-regular graph over 8 green numbers. The puzzle then solves very nicely moving generally from left to right. Except for finding the key and how to use it, which can rightfully be called ridiculous, the rest of the puzzle was no more than reasonably hard. A good Sunday puzzle.

4. MellowMelon Says:

That’s my impression exactly. I really don’t expect many people to find the graph problem hidden in the puzzle on their own, especially as a first step, but after that’s out of the way it does turn into something very doable. Thanks for the comment.

5. rob Says:

Solved it. I did find the graph problem, but I drew some wrong conclusions from it that ran me into a contradiction twice (around the NW diamond). Third try, working that contradiction the other way broke in.

I don’t think the graph problem can be saved on its own, can it? I think you also need the intersections between edges (i.e., of any two intersecting edges, one must be lit). But then, my graph deductions were wrong, so I’m not that sure about this.

• MellowMelon Says:

The graph problem does require not only the intersection condition, but also some extra solving information from the actual puzzle. You can get enough information out of it to put down a bulb at the start, but you need to make more progress on the main part before you can solve the graph completely.

This might have to do with the contradiction you’re referring to.