Double Dragon 2
(Published on 4. May 2023, 23:10 by Nordy)
Back from a short setting hiatus with a sequel to Double Dragon.
Ever since solving the mesmerizing and ultra-satisfying Misfits by filuta, I have been fascinated by unconventional uses for Killer cage totals. Naturally, my first thought was a snake puzzle :) As always, be careful with your arithmetic—the Double Dragon can lead to some sneaky options.
Rules:
Normal Sudoku: Place the digits 1 to 9 in every row, column, and 3x3 box.
Double Dragon
- Shade some cells to form a single, orthogonally-connected, 1-cell wide snake that does not branch, loop, or touch itself orthogonally (but may touch itself diagonally)
- The two ends of the snake must be determined, and they both contain the digit 9
- Any number in a cell that is shaded by the snake has its value doubled. This applies to both digits and Killer Cage totals
Killer Cages: Within each cage...
- The values of digits sum to the value of the number given in one of the corners
- Digits cannot repeat, but values can repeat (ex: a doubled 4 and an undoubled 8 can both appear in the same cage)
Example: Below is a 6x6 example puzzle that you can solve online (SudokuPad). In the example puzzle, the two ends of the snake both contain the digit 6 (instead of 9).
Solve Online:
Solution code: The digits in Row 5 (the unmodified values) followed by the number of snake cells in Rows 1, 5, and 9 (12 digits, no spaces)
Comments
on 3. April 2024, 18:06 by yttrio
Fantastic puzzle! Working through the 6x6 example really helped to figure out some of the logical steps to look for.
on 8. February 2024, 17:36 by Bankey
Phew, that took some doing!! Definitely a 5* for me, but a fun ride. Thanks, @ Nordy :).
on 3. January 2024, 15:30 by jhow25
I'm a little confused by the example.
In R1C1 cage value is doubled: 4 = 2*1+2. But in R6C1 the 22 cage isn't doubled.
In R4C4 the value of the cage is doubled. So I don't really see when doubling occurs.
—Nordy: Sorry, just saw this! For the example, you can think of any number that is shaded red as doubled. So, for the 22 cage, since the 22 isn’t red, it’s not doubled—that cage sums to 22. In that cage, the 6 and 4 are red, so they are each doubled, but the 2 is not doubled. Thus, the sum of that cage is: 2+2(6)+2(4)=22.
For the cage at R4C4, the cage total is red so that 8 is doubled to give a cage total of 2(8)=16. The sum is therefore 5+2(3)+1+2(2)=2(8). The 8, 3 and 2 are all doubled.
on 9. May 2023, 23:23 by Bootenks
Brilliant setup. I really liked to discover the snake path.
on 9. May 2023, 22:48 by KNT
Now that's an arithmetic exercise if I've ever solved one..
on 7. May 2023, 08:15 by filuta
oh wow, that was really cool, some of the cages worked pretty incredibly, esp boxes 7 and 9.
on 7. May 2023, 00:08 by mnasti2
Very good and intricate!
on 6. May 2023, 18:01 by twobear
Very nice. Thank you!
on 5. May 2023, 18:54 by mathpesto
Very impressive setting! A fun challenge, and I love the role of the killer cage sums potentially doubling in addition to individual cells :)
on 5. May 2023, 17:24 by TNGuy
very nice puzzle! Thanks!
