Δ Polygon Doppelganger
(Published on 14. February 2024, 21:31 by KenGlue)
The puzzle uses a special ruleset created by Kafkapharnaum, who also helped in the setting of this one.
DOPPELGANGER
– Every row, column, and box contains the digit 0 always, as well as eight out of the nine digits from 1 to 9 (ie, it's missing one digit that is not 0)
– No two row, no two column, and no two box may be missing the same digit
– For each 0 in the grid, the digits missing in its row, its column, and its box must be three different digits (and note that a zero always acts as itself – ie, the lowest possible value – regardless of what digits it's replacing in its box, row and column)
SKYSCRAPERS
– Numbers in the grid are skyscrapers with length equal to that number. Clues outside the grid count the amount of visible skyscrapers from the direction of the clue, where teller buildings block vision of shorter buildings.
– For the sake of this puzzle, skyscrapers of length 0 are also counted.
NUMBERED ROOMS
– The digits outside the grid are also numbered rooms clues. The number in the clue must appear in the Nth cell in the direction of the clue, where N is the digit closest to the clue.
– If N=0, then the digit in the clue does not appear in the row/column of the clue.
TRIANGULAR PRODUCT LINES
– Adjacent cells along the lines must multiply to a triangular number.
– Triangular numbers are results of the formula n(n+1)/2, where n≥0. (i.e. sum of the digits from 0 to n). (0,1,3,6,10,15...)
............................................................................
Example Puzzle
Solution code: Row 2 of the solved grid (9 digits)
Comments
on 12. August 2024, 12:33 by The Book Wyrm
Nice puzzle!
Interesting combination of rulesets and some neat logic. Not as tricky as it looks to get started.
on 26. February 2024, 22:14 by Kafkapharnaum
Truly great 4x4 example you've added there, very elegant and a perfect warmup I'd say. Hopefully it'll warm up some more solvers to the approach, but in any case, it's already great to see all the activity on this one today, wow. Congrats!
on 26. February 2024, 20:34 by chrisj50
Once I’d got my head around (/properly read and understood) the rules this was great fun. It looked monstrous at first, but the interplay between the rule sets led to a generous start & very pleasing progress. Great debut DG!
on 26. February 2024, 17:22 by KenGlue
Added example puzzle.
on 26. February 2024, 17:01 by wullemuus
Congrats to your first puzzle with so well combined, interesting rulesets! The only trap was "adjacent" in the triangular lines- the rest of the solving path was very smoothly constructed. Keep on going!
on 26. February 2024, 14:34 by bodemeister
Welcome to LMD and thanks for the puzzle! I'm more of a killer sudoku guy, but it was fun to venture out of my comfort zone a little. The triangular product lines is a good choice for patterns. One can even create a 6-cell loop of distinct nonzero digits!
on 26. February 2024, 05:13 by KenGlue
Gave example to prevent ambiguity.
on 16. February 2024, 13:08 by gfoot
Nice job, a great puzzle that is also quite approachable!
on 15. February 2024, 16:48 by marcmees
nice debut. thanks.
on 15. February 2024, 00:17 by Kafkapharnaum
How about that, the double! Glad to see this one uploaded here too, it absolutely deserves it. While the ruleset is seriously intimidating, the combination of Skyscrapers and Numbered Rooms clues actually makes for a surprisingly generous start, and the Triangular Product Lines (a first on LMD, I’m pretty sure) are a friendlier variant than one might think too. Excellent work even just thinking of combining all of this, let alone making such a great approachable 9x9 Doppelganger out of it. Bravo for setting this, and thanks for using the ruleset and sharing the puzzle!
