Logic Masters Deutschland e.V.

Story

Panic in the planet Palin planetarium! The nanobots have evolved to be invisible to our security detectors, and these phantom pests have been propagating prodigiously! Can you deduce their locations and defeat this menace?

Rules

Normal sudoku rules apply. Place the digits 1-9 once each in each row, column, and 3x3 box.

Triangular Sum Lines: On each line, the triangular number of one of the digits is equal to the sum of the triangular numbers of the rest of the digits. The digits 1, 2, 3, 4, 5, 6, 7, 8, 9 have triangular numbers 1, 3, 6, 10, 15, 21, 28, 36, 45 respectively. Digits may repeat on a line if other rules allow.

Counting Circles: The digit in each circle counts the number of times that digit appears in circles, including itself.

Maximum Black Kropki: In each pair of cells joined by a black kropki dot, one digit is double the other. The puzzle solution has the maximum possible number of black kropki dots in any solvable sudoku grid. None of them are shown. It is up to the solver to find them. It is not necessary to know how many there are to solve the puzzle.

Credits

This puzzle is a direct adaptation of replies to my inquiry on CTC discord by Ben, zzw, sigh, and pieguy about maximizing the number of black kropki dots in a sudoku.

Play in SudokuPad

Puzzle Series : The Domes of Planet Palin

• "Dome 19" ... nanobots ate the life support control wiring!
• "Dome 11 - Almost Balanced Products" ... return of the nanobots
• "Dome 49 - Triangulation Enumeration Maximization" ... nano phantom bots
• "Dome ?? - Digital Digits Sudoku" ... coming soon to a Raetselportal near you