¿? Mystery products ¿?
(Published on 28. August 2020, 16:32 by Qodec)
Can you find all 4 mystery products that are hidden in this puzzle?
Rules:
- Normal sudoku rules apply, i.e. each of the digits from 1 to 9 needs to appear exactly once in each row, column, and 3-by-3 box.
- There are cages of four different colors. The product of the digits within two cages of the same color must be equal. Part of the solve is to find out which color represents which mystery product. Products of digits in two cages with different colors do not necessarily have to be different.
- Digits cannot repeat within a cage.
Note that the 6 cell pink/purple region in the bottom right is 2 cages rather than 1.
Example: suppose that the digits in the gray cage in box 1 are 2, 3 and 4. Then their product is 2 * 3 * 4 = 24, which is the mystery product of the gray cages. This means that the digits in all other gray cages must multiply to 24 as well. For e.g. the gray cage in box 5 this means there are only three valid combinations: 1 * 3 * 8, 1 * 4 * 6 and 2 * 3 * 4.
You can play this puzzle online using f-puzzles: https://f-puzzles.com/?id=yyvwldom.
Or, if you prefer cages that are labeled with '1' to '4' rather than colors: https://f-puzzles.com/?id=y68e5x2d. (Works best when the 'highlight conflicts' option is turned off.)
Good luck!
Solution code: The 9 digits in column 2 from top to bottom, no spaces, for example: 391265478
Comments
on 10. April 2024, 10:55 by StephenR
Some interesting logic in this one, thanks. Even after I'd made inroads there I found some steps quite tricky.
on 12. August 2022, 21:12 by Playmaker6174
What an absolutely stunning construction, straight into my favorite list. :o
on 1. September 2020, 09:17 by Qodec
Added tag.
on 1. September 2020, 02:03 by SudokuExplorer
Very nice! The interaction of cages was stunning! This is second time I've tried a puzzle with product cages, and both times they were very enjoyable. I did find this one more approachable than the other one. If anyone likes this variant then they may also enjoy joecat's Rainy Day Sudoku (id=0003ZU).
Also please do add the German "Produkt" tag, so that people can find similar puzzles (or find this one via a similar puzzle).
on 29. August 2020, 12:20 by Qodec
Decreased difficulty.
