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09 December 2011 @ 12:01 am
Friday Puzzle #130 - Caves (DD Part 2)  
I've mentioned before, under the USPC-appropriate name "Corral", that this is one of my favorite classic puzzle styles. So it was an obvious inclusion on my Double Decathlon test and will likely appear again in the future when I'm writing sets of puzzles. I tried here for a visually interesting small puzzle (just two digits accomplished this), and then a meatier hard puzzle that was certainly inspired by my favorite Cave (Corral) of all time.

Rules: Draw a single closed loop that does not touch itself, even at a point, along the grid lines with all the numbered cells inside the loop. Each number equals the count of interior cells that are directly in line (horizontally or vertically) with that number's cell, including the cell itself.



It is rather rare to see 3 touching clues in a Cave puzzle but when you do they are really key spots to work from. Off the edge, you can apply an "all for one, one for all" kind of cell counting for them and that should get you started. The final step is a bit fidgety between one of two options, but there is just the one solution.

The construction of the hard puzzle started from the four spots in yellow in the following image, so your solving should focus there eventually too. The key consequences come from the two diagonally adjacent clues in the lower left corner and upper right corner. Specifically, at least one of the squares in orange must be inside the cave in each corner, which means neither of the yellow 8's can be reached by the yellow 10. This sets up a push/pull in the relevant rows and columns as you carve out just enough squares to satisfy the 10, the two 8's, and leave enough room for the 5. If you focus your thinking on those squares while using the strategies I've given before for Corral, you should be able to manage this puzzle just fine.

cyrebjr: Numberscyrebjr on December 9th, 2011 10:34 pm (UTC)
The easy puzzle has a nice theme. But why is R1C6=5 and not 4?
motrismotris on December 10th, 2011 02:09 am (UTC)
Obviously because I didn't have a style tester like you to fix it before initial release :).

Looking back at my construction notebook, I always had a 5 at R1C6 (and a 4 at R8C3) as I was trying to get a valid middle of appropriate difficulty. This eventually needed the R8C3 # to change, but I missed the flip on the opposite side which certainly works. That's what constructing too many puzzles under too short a deadline will sometimes do.