Rainy Night
(Eingestellt am 6. Dezember 2021, 17:17 Uhr von FryTheGuy)
Back when I created my ill-fated unrated puzzle contest, SudokuExplorer recommended joecat's puzzle Rainy Day Sudoku.
That puzzle quickly became one of my all time favorites, and after revisiting it recently I had an idea for something new I could do with the constraint.
I really like how this puzzle turned out, it is one of my favorite out of all the puzzles I have created so far. It is a very difficult puzzle though (especially for anyone who has not solved Rainy Day), so I provided a very long hint with some of the deductions required to get started.
RulesNormal sudoku rules apply.
Digits cannot repeat in a cage.
The numbers in each cage have a product that is a multiple of 144.
Solve the puzzle at f-puzzles
Hints
There are 15 cages, each cage needs to multiply to at least 16. This can either be accomplished by having an [8] in the cage + a [2],[4], or [8]. Alternatively, it can also be accomplished by not having an [8] and having [2],[4], and [6] all in the cage.
There are 27 [2,4,6] digits in the grid. To maximize the efficiency of allocating the [2,4,6] digits we need to put every [8] in a cage. This leaves us with 18 remaining [2,4,6] digits and 6 remain cages. Since each of these remaining cages use 3 [2,4,6] digits, this allocation uses all of the even digits.
This means that every even digit is in a cage, and every cage with an [8] has exactly one additional even digit in the cage.
There are 15 cages, each cage needs to multiply to at least 9. This can either be accomplished by having a [9] in the cage, or by having a [3] and a [6].
Nine of the cages have an [8] in them. At most 3 of those cages can have a [6] in it since the remaining [6] digits must go in the [2,4,6] cages. This means at least 6 of the cages with an [8] but without a [6] must have a [9] in them.
One [9] must exist outside a cage in box 5, since all the caged cells in box 5 must be even (since every even digit is in a cage).
Two other [9] given digits exist in cages that have 6s in them, so they cannot be the cages with an [8] but without a [6]. We only have six [9] digits left, which means every other [9] is in a cage with an [8] but without a [6]. This means that every cage besides the cages with the given 9s and 6s must contain either a [6] or [9] but not both, and the cages with a [6] must also contain a [3]. This also means that these cages must contain either a [3] or a [9].
There are seven cages with a [6] but without a [9]. There is one [3] not in a cage in box 5. This means that either there is one cage with both a [3] and a [9], or there is a [3] in the uncaged cell in box 9.
Lösungscode: Column 5 and Row 9
Kommentare
am 5. Februar 2023, 23:15 Uhr von filuta
Really brilliantly constructed! Felt considerably easier to me than the Rainy day, but complex enough it should make the original way more approachable. And also still a nice challenge even after solving the the Rainy day. And most importantly - great fun!
am 13. Mai 2022, 23:48 Uhr von Vebby
Wow, great puzzle! Loved the concept, I'm eager to try joecat's puzzle soon now :)
am 21. April 2022, 11:50 Uhr von Phistomefel
Many thanks for this wonderful puzzle, FryTheGuy! Now I might be ready for joecat's Rainy Days.
am 4. Januar 2022, 00:31 Uhr von bosjo
Absolutely brilliant puzzle! I loved every bit of it, from the initial "global" hunt for clues to the final disambiguation of the "unproductive" digits. Fantastic!
It's half past midnight here, and the rain is pouring down -- let it rain a week, please...!
am 17. Dezember 2021, 01:23 Uhr von joecat
Very nice! This took me way longer than it ought...
am 10. Dezember 2021, 01:24 Uhr von Piatato
A fantastic puzzle! I hope that both puzzles will get the dazzling ratings that they deserve! :-D
am 8. Dezember 2021, 16:13 Uhr von DVFrank
Very very nice puzzle with such unique logic! This was still surprisingly difficult even after solving Rainy Day first. I really hope to see more of this type of constraint around :^)
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Glad you enjoyed it, and I am also happy to see that you solved Rainy Day first :)
I think I might be able to make a cool puzzle where the cages either sum to the provided total or their product is a multiple of the provided total.
am 7. Dezember 2021, 08:46 Uhr von cdwg2000
Very nice!
am 7. Dezember 2021, 04:41 Uhr von FryTheGuy
@polar
Glad you enjoyed it :)
My original goal was to make an approachable puzzle with this constraint, but abandoned that idea once I found the logic I ended up using in the puzzle.
I might still try and make an introductory puzzle that just requires a multiple of 16 at some point.
am 6. Dezember 2021, 22:25 Uhr von polar
When I said on joecat's puzzle that it was the sort of puzzle I would love to do again, I didn't think it would actually happen!! I cannot thank you enough for this wonderful puzzle & tribute. Super smooth & enjoyable solve (without rogue cages to contend with this time phew).
