Midpoints
(Published on 23. November 2021, 07:11 by SSG)
Consecutive pairs: Cells separated by a white dot must contain consecutive digits. Not all white dots are given.
Midpoints: The shaded cells contain one set of the digits 1-9. For each shaded cell there are pairs of cells in the grid such that the shaded cell is at the midpoint of the line connecting the pair and the digit in the shaded cell is the average of the digits in the pair. The number of such pairs for a given shaded cell is equal to the smallest prime factor of the digit it contains (to avoid ambiguity, there will be exactly 1 pair for the 1). The following graphic demonstrates three possible pairs.
A 6x6 puzzle demonstrating this ruleset can be found here: https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=00099S
This puzzle can be played here:
f-puzzles: https://f-puzzles.com/?id=ye7g7z66
SudokuPad: https://sudokupad.app/ob340w1w0r
Solution code: Row 9 + Column 6 (18 digits)
Comments
yesterday, 12:32 by Qodec
What Fool on Hill said. Incredible puzzle.
on 26. November 2025, 10:08 by Fool on Hill
This is a beautiful puzzle with an interesting rule which deserves more solves and a rating. It takes a bit of getting used to and thinking through, but the logic is clean and tight. Highly recommended.
on 25. November 2025, 17:03 by SSG
Created a new SudokuPad link that includes solution checking.
on 13. March 2022, 23:19 by ICHTUES
Fantastic puzzle and very cool ruleset too. Once I've got my head around it, it isn't that hard anymore.
The puzzle deserves more solves!
-Thanks! I'm quite fond of this one myself. -SSG
on 4. March 2022, 07:31 by SSG
Added sample graphic and link to Mini Midpoints.
on 23. November 2021, 21:46 by henrypijames
Really tight solution path, 3½ stars difficulty for me.
on 23. November 2021, 19:34 by Siebuhh
Very nice puzzle! I expected some bifurcation but it was not necessary, counting pairs was enough
on 23. November 2021, 11:53 by steelwool
I don't understand how 9 is placed. The smallest prime factor of 9 is 3, I cannot see anywhere I can place 3 lines. Am I misunderstanding something?
-It is possible to place three pairs of digits that have the proper relation to the shaded 9. -SSG
-- oh, of course it is! Devious, I like it (now it just got much harder!)
