The inconvenient square root (chaos construction)
(Published on 19. December 2021, 13:30 by filuta)
I think this puzzle is hard enough even if you know complex numbers backwards and forwards. If you are not familiar with them, you can check out the text at the bottom of the page, which should cover the knowledge necessary to solve the puzzle.
Big thanks to ctc discord users Piatato and Hapuzki for their test solves and feedback and to Piatato also for the penpa link.
Finally (as always) I will be happy to read your comments.
Rules: Standard irregular sudoku rules apply (put the set of digits 1 to 9 in every row, column and region), the regions, however, must be deduced by the solver. All regions are orthogonally connected and some region boundaries are already given and must be respected.
There are three types of regions: positive, negative and imaginary. For the purpose of evaluating the cages:
-numbers in negative regions count as negative (i.e. 3 counts as -3, 7 counts as -7 and so on),
-numbers in imaginary regions count as multiplied by the imaginary unit i (i.e. 3 counts as 3i, 7 counts as 7i and so on),
-numbers in positive regions count as usual.
The number in the upper left corner of the cage shows either the product or the sum (or both) of the digits in the cage (using the usual complex number multiplication/addition).
The digits are allowed to repeat in cages if they belong to regions of different type (so 3,-3 and 3i may all be in one cage, if allowed by sudoku rules, but two -7s are not allowed).
No two regions of the same type may share an edge.
Solve online:
ctc app link (you might need to disable conflict checker and check on finish)
penpa link (with answer check)
f-puzlles link
Brief introduction to complex numbers:
The only essentially different component of complex numbers is a new number "i", which is defined by the property that i*i=-1. Every number has then two components, usual real number (so-called real part) and another real number (imaginary part) which is multiplied by i. The general form of a complex number is therefore a+bi (for some real numbers a and b).
Luckily, in this puzzle, you will need to add/multiply only very special complex numbers (±1,±2,...,±9) and (i,2i,...,9i).
When summing those numbers we just sum real ones separately and imaginary ones separately:
3+4i+(-7)+6i=-4+10i.
When multiplying them, we just replace pairs i*i by -1 and otherwise multiply normally:
4i*(-2)*i*3i=4*(-2)*3*i*i*i=(-24)*(-1)*i=24i.
As an exercise you can try to list all options of a 2-cage which has -3 in the upper left corner (highlight the text below to see the answer).
1) sum of two negative numbers (-1, -2)
2) product of one positive and one negative number (1,-3, or 3,-1)
3) sum of one positive and one negative number (1,-4, up to 6,-9)
4) product of two imaginary numbers (i,3i)
Solution code: column 5 and row 5 (without a comma or a space)
Comments
on 26. May 2024, 11:25 by Styku
Brilliant idea and setting. I loved it from start to finish :)
on 8. April 2024, 16:50 by Agent
Fantastic puzzle! This had everything: some original arithmetic and law of leftovers logic to get started, followed by a really clean region building and irregular sudoku.
on 13. February 2024, 22:56 by zzw
Super cool, so fun and smooth!
on 13. February 2024, 22:55 by Myxo
Wow! That was stunning, amazing puzzle!
on 13. February 2024, 22:54 by wisty
Beautiful, fun, and cozy puzzle! Thank you so much!
on 13. January 2024, 23:22 by wullemuus
What a masterpiece! Thanks to your support I could enjoy the beautiful and narrow path (due to the excellent choice of clues) through this composition!
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you are welcome, really glad you liked it so much
on 1. January 2024, 20:35 by chameleon
Brilliant puzzle! There should be more puzzles with complex numbers in the world!
on 2. April 2023, 11:38 by lerroyy
Great puzzle!
on 4. July 2022, 11:29 by Vebby
Awesome! Loved it! :D
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THank you, means a lot to me cause I feel I really found the right balance of all the aspects in this one.
on 21. April 2022, 06:30 by thefallenrat
Another INNSSAAANEEEE puzzle!! I think my IQ went up a bit after solving this
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haha, nice, thanks a lot for such a funny (and kind) comment
on 9. February 2022, 18:14 by kolot
Wow! I finally solved it without getting help. It was really very hard but very satisfying puzzle.
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Thanks a lot, I'm happy you preserved!
on 3. January 2022, 08:36 by Statistica
Absolutely great! Nice logic path and clever clues.
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Thanks a lot for such a kind comment.
on 29. December 2021, 18:58 by MagnusJosefsson
Great puzzle! Extremely challenging, but with some very rewarding moments when you finally find the intended path forward. Some very interesting logic both in the chaos construction part and in the irregular killer sudoku.
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Thanks a lot for the comment, it really makes me happy, you found the puzzle so rewarding.
on 21. December 2021, 06:17 by kolot
I liked this idea. I spent more than 90 minutes on this puzzle and could place only 3 digits. I failed in solving the last 3 puzzles I attempted. I hope Simon attempts this one. I would like to watch how to solve it.
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Thank you for giving it a try. It's probably quite unlikely likely Simon will pick this one, but in case you are interested, just write a hidden comment, I will be more than happy to provide you with a hint/solution path.
on 20. December 2021, 18:08 by Jesper
Very challenging, but with some brilliant deductions. Very rewarding to complete the solve.
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Thank you so much for such a nice words, I'm happy you found it rewarding.
on 19. December 2021, 18:34 by polar
Wow what a puzzle! Very challenging throughout, but a lovely logical path all the way to the end. Thank you for constructing this beast!
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Oh, thank you so much for such a nice comment, I'm glad you enjoyed it.
on 19. December 2021, 15:11 by Piatato
Really a fantastic puzzle! Thanks for making it, and thanks for giving me the opportunity to learn something new! :-D
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Thank you, I am really happy you liked it so much. And once again, thanks for the test solve.
