X-Sums Fillomino #3 (4x4x4)
(Published on 15. March 2021, 19:53 by Jesper)
3D Fillomino rules apply:
- Divide the space inside the 4x4x4 cube into shapes consisting of orthogonally connected unit cubes
- Each unit cube must contain a number equal to the number of unit cubes in its shape
- Two shapes of same size may not connect orthogonally
Additionally: clues on the surface of the 4x4x4 cube (shown with grey background) indicate the sum of the first X digits inside the cube in the corresponding direction, with X being the first digit in that direction.
As in standard Fillomino, any positive integer is allowed, however a number X (next to a clue) cannot exceed the size of the cube (in this case 4).
Example (3x3x3) – outside 3D view (showing clues):
Example (3x3x3) – layer by layer view, including solution:
For the example, the solution code would be 225772174.
The puzzle (4x4x4) – outside 3D view (showing clues):
The puzzle (4x4x4) – layer by layer view:
Link for solving online:
Penpa+
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Solution code: The numbers in the bottom layer, from left to right, top to bottom (based on the orientation shown in the layer by layer view)
Comments
on 29. November 2023, 20:53 by Playmaker6174
Absolutely amazing (yet twisted) puzzle!
The ruleset provides some of the weirdest scanning I've seen in a fillomino puzzle, but it was so delightful to see how each region was done one-by-one using the interactions between the layers. I especially loved how the ending was resolved too (it was quite tricky to figure it out but also a jaw-dropping part as well ) ;)
on 20. October 2022, 00:26 by Christounet
3D ? Really ?
How about a 4D puzzle next time ? ;)
Very fun concept ! I was actually able to visualize the cube in my head, rotate it, see through it... which may be a sign of mental sanity or insanity, depending on the point of view.
Thanks for this mind-rotating experience !
on 31. December 2021, 00:29 by polar
This puzzle was great fun! Very much enjoying my masterclass from 0 to 100 in solving fillominos!
on 8. September 2021, 09:06 by Vebby
Wow, amazing concept! Pleasure to solve. Thanks Jesper! :)
EDIT @Vebby: I should rather thank you for solving so many of my puzzles and providing nice feedback! Not everyone feels comfortable with 3D puzzles, so I am glad that you enjoyed this one! :) /Jesper
on 7. April 2021, 15:02 by Mark Sweep
Awesome puzzle! I held off solving this one for a while, because I couldn't wrap my head around the 3D rules, but once I did, the logic actually unfolded very nicely! In case others are also struggling to visualize it: colouring may help. For instance giving all completed regions a certain colour gave me a better overview.
EDIT @Mark Sweep: thanks! I do think that 3D risks scaring people off, so I'm really happy that you decided to take the puzzle on. Incidentally, the advice that you gave concerning colouring completed regions is exactly what I used during test-solving :)
on 19. March 2021, 16:55 by MartinR
Nice way of adding a new dimension to fillominos - looking forward to what #4 will have :)
EDIT @MartinR: Thank you very much! I very much appreciate all the solves and comments that you provide on my puzzles! I'm not sure yet about #4. I might re-visit this rule-set in the future, but right now I am working on a different Fillomino hybrid concept, which I think looks quite interesting.
on 16. March 2021, 08:15 by spxtr
Very fun puzzle. I liked that it started off easy and got progressively trickier, since it made it feel very natural to get the hang of the rules. Looking forward to #4 :)
EDIT @spxtr: Thanks! I'm really happy that you enjoyed it!
