Six-pack Linked Sudokus #10 - Sums
(Eingestellt am 30. September 2022, 16:30 Uhr von Genomico)
A number in a circle is the sum of the outside clues of both adjacent puzzles. Digits used for this sum may not repeat.
An empty circle must contain a number from 1 to 21. A circle can only contain one number and also for this sum the digits used may not repeat.
Normal 6x6 sudoku rules apply to all sudokus, so every row column and region must contain the digits 1 to 6.
Additional rules per variant:
1) Next-to-6 sum Sudoku: Clues outside the grid indicate the sum of all direct neighbours of the digit 6 in the respective row or column. Only the adjacent digits in the same row or column as the 6 are counted for the clue, so the clue is the sum of either 1 (when the six is at the border) or 2 digits.
2) Skyscraper sum:: Digits in the grid represent skyscrapers of that height. Higher skyscrapers obscure smaller ones. A clue outside the grid is the sum of all visible skyscrapers in the corresponding row or column from the clue's direction of view.
3) Sandwich sum: Clues outside the grid indicate the sum of the digit(s) placed between 1 and 6 in the corresponding row or column.
4) N-sum: Clues outside the grid indicate the sum of the first N cells in the corresponding row or column from that direction, for some value of N from 1 to 6. N can be different values for different clues.
5) Grey cells sum: Clues outside the grid indicate the sum of the digit(s) in the grey cell(s) in the corresponding row or column.
6) Edge sum: Clues outside the grid indicate the sum of the first two digits in the corresponding direction.
Digits used for a sum clue may not repeat, for example:
- When 10 is in the circle between the Sandwich sum and Edge sum sudokus and the digits 2 and 3 are between the 1 and 6 in the Sandwich sudoku, then 2 and 3 may not occur in the first two cells in the corresponding direction of the Edge sum sudoku and therefor those cells must contain 1 and 4.
- The first digit seen from a N-sum sudoku clue can never occur in a grey cell in the same row (because N is always 1 or more). When N is 3 (i.e. sum of the first three digits starting from a clue's direction) those three digits cannot be used in the adjacent grid.
I think the logic and the interaction between the puzzles are really nice. I hope you like it as well. Enjoy solving! :)
The puzzle is also available on Penpa.
Lösungscode: In the following order (from left to right or top to bottom):
- The 4 numbers in the empty circles in the middle row of the grid.
- The 2 numbers in the empty circles between N-sum and Grey cells sum.
- The 4 numbers in the empty circles between Grey cells sum and Edge sum.
- Row 6 of the N-sum.
- Row 3 of the Grey cells sum.
- Row 3 of the Edge sum.
Kommentare
am 8. April 2024, 21:03 Uhr von Myxo
Awesome puzzle!
am 23. Dezember 2022, 07:01 Uhr von Agent
Very impressive construction! The interactions between the sub-grids were really clever, with a nice variety of logic. And resolving the remaining pairs was very satisfying.
am 22. Oktober 2022, 10:52 Uhr von Silverstep
Awesome puzzle! Took me just under an hour. It gets easier once I think of each clue as a killer cage, the cells of which don't have to be connected, and their positions are determined by the variant rules.
Will go and check out posts #1 to #9 after this.
am 5. Oktober 2022, 07:01 Uhr von Blake Saligia
Ingenious construction!
am 1. Oktober 2022, 12:39 Uhr von marcmees
very nice. smooth solve although I first took a wrong turn on the grid GC R6C3. Thanks.
am 30. September 2022, 23:47 Uhr von Jesper
Very nice, impressive construction!
am 30. September 2022, 18:47 Uhr von Playmaker6174
Holy moly, that was outrageously incredible construction, so many beautiful deductions throughout, especially when it came to dealing with disambiguating those pesky deadly patterns. Thank you for this masterwork as always ;)
Reply: Thank you very much for those kind words and I'm very happy you enjoyed the Six-pack again :) And gratz for being the first to solve it ;)
am 30. September 2022, 18:41 Uhr von ClashCode
So to clarify for N-sum:
If N is 3, all the digits are included in the sum.
However, for the purposes of clue digits not repeating, only the 3 is included?
Reply: If N is 3, the first 3 cells are included in the sum.
am 30. September 2022, 17:36 Uhr von coldfrog
Can you clarify regarding the Next-To-6 sums - the numbers for the sum are only the ones adjacent to the 6 that is in that row? As in, if the 6 in row five is touching a 2 in row five, and the 6 in row six is touching a 5 in row five, only the 2 is counted for the sums of row five, is this correct?
Reply: Thank you for your question. You are right. Only the adjacent digits in the same row as the 6 are counted for the clue. I'll clarify in the rules.
