Bimathlon (Duality)
(Published on 11. January 2024, 05:33 by starwarigami)
Lines are both Product-Sum Lines and Zipper Lines.
- Along a line the product of the digits in the two connected squares is the same as the sum of the digits between the squares
- Digits on the line an equal distance from the centre of the line sum to the same value. For a line of odd length, the digit in the middle cell is equal to that value.
- Digits may repeat on a line if permitted by other rules.
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If you enjoyed this puzzle, please check out the previous puzzles in this series
Solution code: Column 9, top to bottom (9 digits, no spaces)
Comments
on 12. January 2024, 09:19 by Piatato
Excellent!
on 11. January 2024, 18:37 by anyeyeball
Enjoyable puzzle. Very nice logic with the carefully placed lines.
on 11. January 2024, 07:28 by starwarigami
Updates rules for clarity
on 11. January 2024, 06:26 by Nylimb
Could you clarify the rules? Do the digits in the squares count as parts of the line for the product-sum and zipper conditions?
E.g. which of these is a valid product-sum line: 47896 or 42576?
And for zipper lines is the sum of the digits in the squares supposed to equal the other sums of digits at equal distance from the center?
P.S.: I wrote a small python program to explore the possibilities. Based on that I guessed that the squares count as part of the line for the zipper rule but not for the product-sum rule. After a while I figured out the solution.
Thanks for the puzzle.
@Nylimb: Thanks for trying the puzzle out - If this is your first time encountering product-sum lines I can understand your confusion with the wording above. I've updated the rules in the description above to clarify the constraint, and will keep it in mind for future puzzles.
@starwarigami: Thanks. I think this was my first product-sum lines puzzle.
Thanks again for the puzzle; once I figured out the rules it was a very enjoyable solve!
