Logic Masters Deutschland e.V.

This puzzle was set for the second round of Agent's Puzzle Agency Championship. The prompt for this round was to create a puzzle with 3x3 clones that clone exactly two of numbers, lines, and cell coloring.

Normal sudoku rules apply.

Lines: Draw two non-branching lines in the grid - one green and one blue - that connect the centers of cells. The lines must only move orthogonally (i.e. not diagonally). Neither line may touch itself, even diagonally. The two lines may, however, touch or cross each other, but only at discrete points (i.e. extended segments may not coincide). The green line must form a closed loop; and, the ends of the blue line may not be on intersections with the green line.

Projected Sums: Clues outside the grid give the sum of digits on lines along the indicated direction. Colored clues count only the line of that color. Black clue count digits on both lines. If both lines pass through a cell, that cell's digit only counts once in the projected sum.

German Whispers: Along the green line adjacent digits must differ by at least 5.

Modular Lines: Along the blue line, every run of three digits must all have different remainders under division by 3.

Clones: The two cages are exact clones of each other. They contain the same digits in the same positions and they contain the same lines (including color) in the same positions. Digits may repeat within the clone if otherwise allowed.

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