Product Killer Sudoku
(Published on 24. July 2020, 13:13 by emmettcito)
All standard sudoku rules apply. Additionally, the digits in each cage sum to the product of the highest and lowest digit in that cage. Digits cannot repeat within cages.
Finally, cells with a line between them must be nonconsecutive.
The product the cage sums to is always a product of two numbers even if the highest and lowest digit are the same number. So a single cell cage with the digit 3 for example would need to sum to 3 squared which is 9, which would make it an invalid digit.
Solution code: 3rd and 6th rows
Comments
on 25. July 2020, 00:51 by henrypijames
After filling all but one cage with candidates, I got stuck and had to bifurcate. Would love to know the logical path there.
on 24. July 2020, 19:52 by RockyRoer
Yikes... finished to find an unresolvable 56 pair. Returned to re-read directions. NON-consecutive. Grr... I read that wrong. My bad.
But I think the 1-cell cage, after the proper explanation, was on point and on theme and should stay that way.
on 24. July 2020, 19:40 by SenatorGronk
Nice puzzle.
I know you probably wanted to avoid having any starting digits in the grid, but I think it'd be preferable in this case so you could avoid the extra explanation for the 1-cell cage.
on 24. July 2020, 18:29 by emmettcito
@RockyRoer When I began setting this the first thing I did was computer test all possible combinations and found that 6 or more digits in a cage is impossible. It is also not to difficult to prove that fact without use of a computer.
on 24. July 2020, 18:15 by FlareglooM
Nice one, thank you for the puzzle :).
on 24. July 2020, 17:29 by emmettcito
@RockyRoer there is actually only one digit that the single cell cage can be, as the one number is both the highest and lowest digit in that cell, which means that the sum of that cage must be that digit squared. I perhaps should have been a little clearer about that
Also for anyone who is stuck here is a HINT: there are not many valid combinations of digits that can fit into the cages and finding those combinations is easier than you think it is.
