Equality Cube
(Published on 4. December 2023, 00:56 by Sniglett)
Puzzle made in collaboration with gUBBLOR. For a lower difficulty puzzle with the concept, try Equality Cages 114: Now in 3D!
Normal sudoku rules do NOT apply. The grid consists of 4 differently colored 4x4 layers. Each layer can be stacked on top of each other in reading order to form a 4x4x4 cube.
Each layer contains a unique digit set from the following, to be determined by the solver; Even (2,4,6,8) / Odd (1,3,7,9) / Low (1,2,3,4) / High (6,7,8,9). Digits within a layer may not repeat in any row, column, or 2x2 box. Digits may not repeat on the Z axis between layers. (ie; R2C2 in two layers may not contain the same digit).
Equality cages: Cages must have an equal number of low (1,2,3,4) and high (6,7,8,9) digits AND an equal number of even (2,4,6,8) and odd (1,3,7,9) digits. Digits may not repeat in a cage. Cages sharing a letter are connected between layers.
Dutch Whispers - Digits along an orange line must differ by at least 4.
Renban - Digits along a purple line must form a consecutive set of digits, but may be rearranged along the line.
Slow Thermo - Digits along a gray thermometer must strictly not decrease from the bulb end.
Sequence Lines - Digits along a teal line must share the same difference with adjacent digits along the line. (ie. 123, 246, 147, 333)
Solution code: Rows 1 and 2 of grid 2.
Comments
on 5. December 2023, 23:15 by Myxo
Very interesting interactions! :)
on 5. December 2023, 21:56 by vitaminz
Figuring out what the bottom left layer was was a top-tier moment for me. Great job!
on 5. December 2023, 15:52 by DadJokes
Nice interactions. Well set!
on 5. December 2023, 01:17 by cam
Excellent puzzle! Four stars for difficulty seems extremely wrong for this. It's more of a coffee puzzle. Nonetheless, it was great and deserves a "very nice" rating :)
on 5. December 2023, 00:51 by femto113
Hard to decide what difficulty this deserves, but four stars seems too high to me. The break in took a while to find but after that the solve went pretty quick once I got the hang of cross referencing layers.
on 5. December 2023, 00:11 by Martini
Nice solve to this one once you understand the ruleset properly
on 4. December 2023, 18:41 by DVFrank
I find the rules about the digit sets hard to follow. What does it mean? Is every layer filled entirely by digits from one of the given groups? Or do we pick one digit from each group for the layer? If so, do these choices for each layer have to be different for every group or just different overall? Or are these sets selected in yet another way?
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Each grid contains one complete set, and each set is used. As an example, if grid 1 is even, it will contain exactly 2468 on that layer, and no other layer will be completely even.
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Okay, thanks for the clarification! :)
on 4. December 2023, 10:35 by roavin
This is such an awesome ruleset. But yeah, it's hard - I ended up opening up a separate text editor to keep track of the combinations of what the layers could be, whittling it down piece by piece until I knew what the layout had to be. The Z-Axis constraint does a _lot_ of work here.
