Half Full Jar
(Published on 25. February 2025, 10:47 by Nimo)
https://sudokupad.app/v382uprxq1 Rules:
Jigsaw
Fill all cells with digits between 1 and 9 so that each digit is exactly once in each row, column and jigsaw region. (The cell with grey are in one jigsaw region!)
Region Sum Line
For each line, digits on the line have an equal sum N within each box it passes through. If a line passes through the same box more than once, each individual segment of such a line within that box sums to N separately.
Hints:
1. Find R1C4 and R9C8, by considering possible sum of regions. Then, three region sum sets in C8 can only be one of the two combinations: (4?)(??8)(??7) or (5?)(??9)(??7). We will use this later.
2. Look closely at R5C234. Find 3 cells that pair with them in R6789. Prove that R5C3=R6C?, then R5C2=R9C?, and both R5C24 are bivalues.
3. From here find more cells that are equal to R5C24
4. Prove that R12C8 are both different from R5C234!! This will reveal R5C3.
5. Use the conclusion in hint 1 on C8 to find R4C7, R5C9, and eventually find R7C6. You will then be good to go.
Solution code: Row 5, left to right
Solved by lmdemasi, ZornsLemon, Ephen, StefanSch, jalebc, MonsieurTRISTE, mihel111, steeto, Chelo, SKORP17, brewring, askaksaksask, SenatorGronk, AzureFire, Bjd, Joyofrandomness, gxorgx, bansalsaab, tallcat, Danica, zlotnleo, Vodakhan , Clara123, Isael, gfoot, Azumagao, Shweebag, dunder, mercierus
Comments
on 25. February 2025, 20:16 by askaksaksask
This is a very fun puzzle! Brilliant logic and a very clever construction. Perhaps you could hide the hints as white text? Otherwise, thank you for this very cool geometric puzzle. The RSL/irregular interaction here is great!
on 25. February 2025, 14:55 by StefanSch
Nice logic!