Trolley Problem
(Published on 28. January 2025, 18:27 by the_cogito)
Rules:
- Draw a single closed railroad (loop) in the grid that travels both orthogonally and diagonally between the centers of touching cells.
- Within the grid, locate "islands" of orthogonally connected shaded cells.
- Different islands may not touch orthogonally.
- The railroad visits every shaded cell and does not visit any unshaded cells.
- The railroad visits every island exactly once, where a "visit" ends when the railroad visits a cell in a different island.
- Assign the following value to cells visited by the railroad: 1 for straights, 2 for obtuse angles, 3 for right angles, and 4 for acute angles. Circled clues on a diagonal outside the grid give the sums of consecutive cells visited by the railroad on their respective diagonal, in the correct order. No clued diagonal is missing clues.
- A "?" represents a single such clue.
- A blank circle represents any number of such clues, including none. - Different clues on the same diagonal must be separated by a cell not visited by the railroad.
Quite a mouthful, I know. I've set a solvable example puzzle to demonstrate the rules and to perhaps offer a chance to build some sort of logical foundation, should you want it:
Solve on Penpa (answer check on line only)
Solve on Sudokupad (no answer check)
The main puzzle:
Solve on Penpa (answer check on line only)
Solve on Sudokupad (no answer check)
Solution code: For every row from top to bottom, the number of acute angles in that row.
Comments
on 2. February 2025, 00:04 by Agent
Very inventive ruleset, thanks!
on 1. February 2025, 15:57 by Agent
Can the question marks represent a 0?
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They can't, I'll have to make updates to clarify that.
on 31. January 2025, 21:10 by Default
Very nice puzzle! The rules seem complicated at first but once it clicks it is quite elegant. Lot of fun to figure out what is possible within these constraints.
on 31. January 2025, 17:35 by the_cogito
Miscounted one row from the solution code, fixed now, sorry!
on 28. January 2025, 19:18 by dumediat
This puzzle is packed with a ton of clever deductions and was a lot of fun! It requires a lot of care and attention to avoid making mistakes, but is well worth the effort!
