Logic Masters Deutschland e.V.

It was the end of a warm Thursday evening. I had just settled down after getting the kids tucked in and finishing the day's chores. The house was quiet, with nothing but the trees rustling in the breeze outside to break the silence. I had just leaned forward to take my last sip of tea when, out of nowhere, I felt a sharp sting across my left cheek followed by a loud THWAP! My face was flung back, and as I recovered and looked up, I saw a hippo...a glum_hippo...standing before me with a glove in his hand. Our eyes met, and he uttered the following:

"You have been challenged, dumediat. Set a puzzle inspired by nanameguri, if you value your dignity."

I rubbed my eyes to make sure what I was witnessing was real, but before I could reply he had vanished. I would have doubted the reality of these events, but I could still feel the sting across my cheek. It seemed that I had a new challenge before me, but there was one question still to ask...What the heck is a nanameguri was in my tea!?"

This is a puzzle that I created as part of the monthly prompt in the Cracking the Cryptic Discord server for August 2023, where I was honored to be challenged by glum_hippo to create a puzzle inspired by nanameguri. Since this is a relatively new pencil puzzle genre, I included a solvable example below that uses the same rule set as this puzzle. This uses modified nanameguri rules, so if you would also like to solve some pure nanameguri puzzles made by various setters those can be found here. Ratings, comments, and feedback are much appreciated! Please feel free to reach out to me on Discord if you have any comments or questions. Please also feel free to try my other puzzles here.

Playable 6x6 example (Penpa+; rules in link): https://tinyurl.com/25fgmvyx

Main puzzle rules:

1. The two grids provided must be considered as a single grid for the purposes of the solve. These have been separated for ease of note taking and scanning.
2. For the left grid, the rules are as follows:
• Nanameguri: Draw lines through orthogonally adjacent cells to form a single loop that does not branch off or cross itself. The loop must visit every cage and every cell containing a diagonal exactly once, and the loop cannot go through diagonal lines. The solver must determine the position of the diagonals. The loop may or may not visit circles.
• A clue outside the grid indicates in how many cells the corresponding shape (+ diagonal, - diagonal, circle) occurs in the row or column. Empty cells provide no such information. Each cell may contain no more than one shape.
• A cell with a circle must contain a sudoku digit that indicates the number of cells containing loop in the (up to 9) surrounding cells in the left grid, including itself. Once a circle is placed in the left grid, it must be transcribed to the same position in the right grid with the appropriate digit.
3. For the right grid, the rules are as follows:
• Normal sudoku rules apply.
• Killer: Digits in cages must not repeat, and sum to the small number in the top left corner of the cage.
• See also the rule above regarding circles.

Main puzzle (Penpa+): https://tinyurl.com/24befqg4

Note: For answer check to work properly, correct loop segments (green), diagonals (green), and circles must be placed in the left grid, and correct circles and sudoku digits must be placed in the right grid. Do not place sudoku digits in the left grid.