Sunday Surprise #12 – Palimpsest Puzzle Set by Nikolai Beluhov
For those who thought there would be no special puzzles on Sundays in 2014: SURPRISE!
This very creative submission comes from Nikolai Beluhov. And like his earlier Matryoshka Fillomino, this is a gift that keeps on giving. Starting with a challenging Fillomino puzzle, erasing all of the 4s leaves a Slitherlink. Then erasing all of the 3s leaves a Tapa. Then erasing all of the 2s gives a Simple Loop (treating the 1s as blackened cells).
Fillomino
Slitherlink
Tapa
Simple Loop
or solve online (using our beta test of Penpa-Edit tools; use tab to shift between a Composite Edgesub mode for Fillomino and Slitherlink, a shading mode for Tapa, a number entry mode for Fillomino, and a line drawing mode for Simple Loop.)
Rules: Standard Fillomino rules.
Then standard Slitherlink rules.
Then standard Tapa rules.
Then Simple Loop rules (draw a single closed loop, without intersections or crossings, through all empty cells; cells with 1s cannot be visited by the loop).
Answer String: None for this puzzle; simply click solved if finished.
Solution: PDF
I have a little mind block.Are all the puzzles solvable individually?!They should be as I don’t see how they could be solved connectedly as a whole?
Yes, there are four separate puzzles to solve. I added in the individual titles now to help you.
Very nice!!
I’m seeing two solutions to the tapa, though. Is anyone else?
Ack, never mind.
15:10,20:20,6:24,6:18.Tapa was an absolute delight!
48:12.
Just creating a set like this is quite an achievement, but all four puzzles are also very good, very impressive. 😀
Very impressive construction!
My fillomino, tapa, and simple loop times were 23:25, 9:40, and 9:10.
On the Slitherlink I was stalled for a long time on a step about half way through, until I finlly tested two ends as connected, (leading fairly quickly to a contradiction), and things went smoothly after that.
-Carl
Very nice. Especially the Slitherlink. I quite liked the Tapa too.
Feels a bit odd not to have to enter an answer key though… I like to have the confirmation that my solution is correct.
– Neelix
I think the Tapa is the most satisfying puzzle — constraining a Tapa to use only 1’s and 2’s (and not 22, 211 etc) makes for an interesting puzzle that makes great use of connectivity. A very impressive design achievement as well, of course.
Was there a technique for the Simple Loop that didn’t require assuming uniqueness? I was quite stuck until I started doing that, and then it fell quickly.
Sure it’s solvable without using uniqueness. If you want to post (a link to) an image of where you got stuck, we can advise you of the next few logical steps?
You can use the Region Parity Theorem, which is explained on my blog. No uniqueness required! http://edderiofer.blogspot.hk/2014/11/on-subject-of-parity-when-we-refer-to.html
Wow Nikolai, where do you come up with the ideas for these?