Logic Masters Deutschland e.V.

• Normal sudoku rules apply.
• To provide each house (🏠 🏠 🏠) with the three utilities they need (gas 🔥, water 💧, and electricity ⚡) draw a line between each house and each of the three utilities (nine lines in total):
  • All lines must be the same length N.
  • Lines may move diagonally, but they may not cross themselves or each other, and they may not share any cells except at their endpoints where they meet at each house and each utility.
  • Lines may not go through any cell with a green circle or any cell adjacent to a dot or red X.
  • Adjacent digits along these lines must have a difference of at least 5.
• The grid is toroidal: each edge of the grid is considered to be adjacent/orthogonal to its opposite edge. (For example, r1c2 is considered to be orthogonally adjacent to r9c2.) Lines wrap around opposite sides of the grid.
• Digits joined by a red X sum to 10. Not all possible X are given.
• Digits joined by a black dot are in 1:2 ratio and digits joined by a white dot are consecutive. Not all possible dots are given.
• Digits on a green circle are odd.

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See also:

• homotopically 3/4
• on elliptic hyperboles