The Postman Problem
(Published on 6. July 2023, 13:16 by ThePedallingPianist)
The Postman Problem
Play on f-puzzles
Play on CTC
Solution Guide
Practice puzzles and their answers
N.B. these do not include the anti-kropki rule, as the 9x9 does. Skyscraper cells are brown, road cells are grey, field cells are green and the route is red.
3x3 --> Show answer
4x4 --> Show answer
6x6 --> Show answer
Rules:
Normal Sudoku rules apply.
The grid is a city, and each cell represents either a skyscraper or a road segment. The digit in a skyscraper cell represents its height in number of floors.
Clues outside the grid show how many skyscrapers are visible from the direction of the clue in that row or column. A skyscraper is visible if it is taller than all other skyscrapers between it and the clue. These clues refer only to skyscraper cells; i.e. road cells are invisible to the clues.
You are a postman. Draw your route, which must be an orthogonally connected loop that travels only on the road and does not branch or enter the same cell twice. In order to deliver post to every floor of every skyscraper as efficiently as possible, your route must visit exactly n of each skyscraper's neighbouring cells, where n is the digit in the skyscraper cell (its number of floors). Neighbouring cells are one orthogonal or diagonal step away.
Your route need not necessarily visit every road cell, and therefore, for ease of solving, a third cell type (e.g. “field”) may be used to show cells that are neither skyscraper nor part of your route.
[The following rules do not apply to the smaller practice puzzles]
The inequality sign points at the lower of the digits in the two cells. You can't afford to waste any time stuck behind any pesky pedalling pianists on their 2 kropki wheels, so make sure that adjacent digits on your route are never consecutive or in a 1:2 ratio!
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If you enjoyed this, please check out my other puzzles!
Solution code: Top row (left to right)
Comments
on 10. September 2023, 21:20 by Al Fresco
Awesome puzzle. Thank you
on 22. August 2023, 14:48 by ThePedallingPianist
Solution guide added
on 2. August 2023, 15:31 by ThePedallingPianist
Links to the main puzzle updated with the new wording of the rules, as shown on this page (the practice puzzles still have the old wording)
on 14. July 2023, 05:40 by marcmees
incredible puzzle. Thanks for sharing.
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Thank you too! It's a pleasure as always!
on 9. July 2023, 16:06 by giladooshlon
Wonderful puzzle and very hard. I was confused for a long time, forgetting it is possible for a skyscraper cell to be hidden behind others and the implications of that fact on the counts.
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Thank you! Yes, it really isn't easy - I'm glad I made the practice puzzles, example and solution guide! Congrats on solving it though!
on 7. July 2023, 12:30 by ThePedallingPianist
Rule clarification (and correction of a spelling mistake - apologies for the misspelling of "visible" in the ruleset within the links themselves!)
on 7. July 2023, 03:41 by henrypijames
1. The rules don't say anything about the route not being allowed to visit skyscrapers, but your example seems to suggest so?
2. Although the route may not branch or cross, it may still visit the same cell twice as in R4C5-R5C5-R5C4 and later R6C5-R5C5-R5C6?
3. The floor metaphor really doesn't work and is super confusing - a neighboring cell representing floor can be shared by different skyscrapers, but how could skyscrapers share floors?!
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Hi, thanks for the feedback - I do find it hard to get the wording of the rules exactly right so I'll aim to be clearer next time!
1. In an earlier draft, I said that cells were either "skyscraper cells" or "road cells", and the route goes along the road. I later cut this out, partly for efficiency and partly because the route doesn't have to go along every non-skyscraper cell. Perhaps I should have reviewed this possible misinterpretation after making that cut, although the rules still say "Neighbouring cells are one orthogonal or diagonal step away", i.e. not 0 steps.
2. That's another misinterpretation I hadn't considered, although to me that would still constitute the route crossing itself. To clarify, the route may only visit any cell a maximum of once.
3. Yes, perhaps the metaphor was a little bit of a stretch... I guess I'm imagining two skyscrapers across the road from each other, and the postman is able to deliver post into the pigeon holes of both of them from the same segment of road... which I suppose begs the question, why couldn't the postman just deliver to all floors in one visit? But hey, it's not meant to be completely realistic!
I'll add in an alternative wording of the rules in the puzzle description for extra clarification. I hope that helps :)
on 6. July 2023, 19:11 by Snookerfan
Absolutely brilliant puzzle as usual! It had a really mean step near the end sudoku-wise or I missed an obvious point. I suspect the latter. I found the rules quite hard to understand, so I was delighted with the practice puzzles and solution to clarify them. Thank you for this masterpiece!
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Thank you again for the feedback and congrats on the solve! There is indeed one fairly hard step late on but if you ask the right question I don't think it's too bad... I'll put it in a hidden comment, hang on!
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You pointed out the exact step I was referring to. It was not mean at all, just tricky and fair! I called it really mean in good spirit, because it took me way too long to find.
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Ah that's great, thank you! Don't worry, I took it in good spirit, I just thought it was worth pointing out because when I first got to that point in the composition (I tend to compose by solving as I go along), I think my way of resolving that was much more long-winded and bifurcatory than it needed to be!!
