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Monday Mutant 19: Process of Illumination / Battleships

Monday Mutants is a series in which I will attempt to experiment with "mutant" puzzles. These could be existing puzzle types with an unusual change in the rules, hybrids combining elements from multiple puzzle types, or puzzle types neither invented nor popularized by Nikoli.
Ten ships (as indicated below the grid: one four-cell ship, two three-cell ships, three two-cell ships, and four one-cell ships) are hidden in the grid. The ships may be rotated from the orientations shown (without changing the numbers), but may not overlap or occupy cells which share a corner or an edge. A number to the right of a row or below a column indicates how many cells in that row or column are occupied by ships. These ships also function as black cells in a Process of Illumination puzzle, and the numbers on some of the ship segments function as they normally would in such a puzzle. None of the black cells already present in the grid are part of the ships. Locate the ships and solve the Process of Illumination puzzle.
If none of the other puzzles on this blog can be considered "mutants", this one most definitely can be.

Speaking of mutants, the day after tomorrow is my birthday! To celebrate, I will be posting more Monday Mutant-style puzzles just for the solving pleasure of you, my dear readers. Of course, since they're going to be posted on a Wednesday, I won't be able to call them Monday Mutants. Nonetheless, I believe you'll enjoy them. :)


Anonymous said...

Haha - you shouldn't let mere things like names of days of the week get in the way of your series! :)

I must say this mutant is an absolutely fascinating idea - really nice!


Marion's Dad said...
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Marion's Dad said...
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Ray said...

Great puzzle Grant! The way that the two different puzzles are intertwined is excellent.

Jonah said...

That was fascinating to solve. I ended up using four colors in my paint program (boat, lightbulb, unlit sea, lit sea), which was more than a little disorienting.

termital said...

I echo the already expressed sentiment - this is a fun, varied and interesting solve. Easily matches the calibre of your Inequality Polyominous.

I had some trouble keeping the rules straight in my head, leading to an early contradiction around the 2nd row. The mental image of beacons floating between ships helped, and painting the grid blue helped reinforce that. Funny how that seemed to clear everything up. For a b&w presentation, I would use a wavy fill in lieu of solid black, and black inner digits with white borders, but enough pernickety presentation points.

Unknown said...


We'll talk.

Anonymous said...

Wow, a great puzzle. I really like how it uses and intertwines theorems from each of the puzzle types, but also requires new theorems and thoughts to complete.

I solved it in paint as well, (although, I only used 3 colors as I'm typically able to keep non-ship squares in my head)

Anonymous said...

Best mutant yet. Half the fun was developing a new language to solve the bugger. Unlike PAINT users, I used a simple very small x or o in the top left corner of each cell to designate bulb or not, and standard big X and darkened big 0 to mark the ships (with numbers in parens ( ) below the ships to mark the neighboring bulbs).

Very fun interaction MathGrant. Well done indeed.


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