Logic Masters Deutschland e.V.

Lupin's Loop 1

No Shared Factors

Backstory

When the city announced a challenge to design a perfect new road system, there was really only one candidate everyone expected to solve it: Professor Lupin, the mathematician so famous for his love of loops that people joked that was how he got his name. He set out to design a single elegant road network — one continuous road that would eventually close into a loop while connecting every house in the city.

Rules

Normal Sudoku rules apply.

Road: Draw a single road that travels orthogonally from cell to cell, never branching, crossing, or overlapping, and eventually closes into a loop. The road must pass through every house.

Traffic Lights: Borders marked with traffic lights are controlled intersections that the road cannot cross.

Segments: The bold 3×3 borders divide the road into segments.

No Shared Factors: Within each segment, all digits must be pairwise prime. That is, any two digits in the same segment share no common factor greater than 1.

Houses: A digit in a house equals the length of the segment containing it.

Speed Cameras: A digit in a speed camera counts how many road cells appear in the entire row of that camera, including the camera cell itself.

Note: A segment does not necessarily contain a house. Any segment of length 1 must contain the digit 1.

Solve Online

This is the first puzzle in a new series, and I truly hope you enjoy solving it. I would be very happy to hear any feedback, thoughts, or comments you may have.