Averaging squares
(Eingestellt Gestern, 11:28 Uhr von Sudokode)
In the past few days, I was experimenting with a new constraint I imagined. However, making the puzzle hold was not easy and I had a few failed attemps. Eventually, I came up with this construction, it's quite hard so I'm looking forward to make an easier version so that everyone can enjoy this constraint.
Good luck on solving this one!
Rules:
- Normal sudoku rules apply : fill each row, column and box with the digits from 1 to 9, each appearing exactly once.
- Averaging squares : A digit in a blue square indicates the average (arithmetic mean) of some of the first digits seen in each of the four orthogonal direction. The number of digits the average is taken from must be determined and might change from one direction to another (Example : if 5 is in a blue square, its row could read ...1-9-5-2-6-7...).
- Extra-region: All squares (blue or grey) contain different digits.
- Black kropki dot: The black dot lies between two digits in a 1:2 ratio (i.e. one is double the other).
Here is the puzzle:
Hope you enjoy it! Any feedback is highly appreciated!
Lösungscode: Row 9 (9 digits)
Kommentare
Gestern, 23:41 Uhr von Myxo
Fascinating that this solves! Not the smoothest solve at times but fully logical.
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@Myxo Glad you enjoyed! I will try to make a smoother version.
Gestern, 19:06 Uhr von PierreTombal
I had some difficulty understanding the rules, figuring that "some of the first digits" might also be 0 digits in at least one of the directions and/or a blue square 5 could also be created from a [1,6] in the row and a [1,2] in the column. The correct interpretation turns out to be that in every orthogonal direction you must have a set of digits that average to the value in the square.
I found the break-in extremely hard to see. Eventually I resorted to creating two versions of the grid, both of which required further complex evaluations until one of them finally ended in a conflict. Reviewing, I still don't see how to to do it without the trial and error (i.e. bifurcation) method.
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@PierreTombal Thanks for sharing your thoughts on the puzzle! I understand that you find the wording of the averaging square rule ambiguous and so I will make it clearer for future solvers. Thanks for pointing out the ambiguities. Also, on certain steps, it is true that you need to rule out a possibility by "looking ahead", but I wouldn’t consider these steps "bifurcation" because you can see the moment it breaks in your head.
