## The Tenth Sandwich - A Satellite Dish

(Eingestellt am 12. Juli 2020, 00:03 Uhr von FlareglooM)

Description
This puzzle is a variation on Sandwich Sudoku. 10 sandwiches have been hidden in the puzzle. Your goal is to find the first 9 based on the 6 given, green colored, sandwich clues. The 10th sandwich is constructed based off the first 9 and will allow you to complete the puzzle.
No digits are given, all of them have to be deduced.
Make sure to read the rules, because the sandwiches are not only "between 1 and 9" sandwiches.

The Puzzle

Solve on penpa-edit.

Rules
• Standard Sudoku rules apply.
• Sandwich Sudoku rules apply with variations/changes.
• The reading direction of the three double digit is given in the example image below. The example values are: 12, 34, and 56.
• The 6 sandwich clues give the totals for 9 hidden sandwiches. The rows/columns/diagonals the sandwich clues operate on are shown in the image below. One sandwich for each arrow/direction.
• The green sandwich clue cells can never be a part of the sandwich.
• The sandwich needs to be a continuous path, without a green cell.
• The sandwiches are allowed to cross over/loop over the edge of the grid.
Example of a 1-9 sandwich with a 25 clue:
• The sandwiches are not restricted to be only between 1 and 9. The sandwiches are between 1 and a value N, with N from 1 to 9. That means there is a sandwich sum between 1-1, 1-2, 1-3 ... up to 1-9. You will need to deduce which sandwich has which N.
• The 10th sandwich needs to be constructed from these nine found "N" values. Concatenate them in the order you find them in the grid when reading from left to right, top to bottom. For the 1-1 sandwich, use the first 1 you encounter.
This will give you a "between 1 and 9" sandwich clue with two totals. These totals need to be used to complete the first 3 cells of row 1 and allow you to finish the Sudoku.
An example of the 10th sandwich, with the green sandwich clues omitted:
• The 9 blue cells represent the "N" value part of the orange cell sandwiches, which you could have found.
When you read off the "N" values and concatenate them you get: 526489317.
Making that into a two way 1-9 sandwich gives the two sandwich totals: 3 and 32 (7+5+2+6+4+8).

Final comments
The 10th sandwich originated from the fact that all constructions I made based on the rule set, resulted in either an unsolvable puzzle or a puzzle with multiple solutions. Of the 50'ish constructions, this was one of the few with a really low amount of solutions and it's the only one that allowed me to introduce anything based on the theme to generate a unique solution. At first I somewhat disliked this 10th sandwich, but now it feels like you find a hidden password and you need to use it to solve the puzzle. It gives a small extra dimension to the puzzle.

The Satellite Dish in the title comes from the fact that, for me, the given green clues look like a Satellite Dish. I also like the way the word Dish fits with the Sandwich Sudoku theme.

In case anyone knows of a similar puzzle, which has a unique solution without introducing an extra thing like I did, I would be very interested to learn about it.

If you have questions/tips/suggestions/remarks/critiques or anything of the sorts, don't hesitate to comment.

Happy solving!

Lösungscode: The first 3 cells of row 1 followed by the nine digits of the 10th sandwich.

Zuletzt geändert am 12. Juli 2020, 00:10 Uhr

Gelöst von MumboJumbo, NikolaZ, MartinR, zorant
Komplette Liste

### Kommentare

am 22. Juli 2020, 21:34 Uhr von MartinR
The ruleset took quite a bit of working out, wasn't clear for a while how 6 clues made 9, eventually worked out that the 2 digit clues only worked in one direction and the single digit ones applied to both a horizontal and vertical clue.
That said, once the rules were grasped, had a logical path, but am still confused how to use the last sandwich clue :)
(Will follow that up in hidden comment to clarify)

Zuletzt geändert am 17. Juli 2020, 11:31 Uhr

am 17. Juli 2020, 11:29 Uhr von FlareglooM
@MumboJumbo
Glad that you managed to solve it.

It looks pretty daunting, while it's actually doable. Maybe that's also because of the presentation of the puzzle. That will be something I'm going to work on for future puzzles.

Thank you for the feedback.

am 12. Juli 2020, 20:17 Uhr von MumboJumbo
Nice one, much less daunting than it looked on first inspection.

Zuletzt geändert am 12. Juli 2020, 00:11 Uhr

am 12. Juli 2020, 00:10 Uhr von FlareglooM
Added comment at the top to read the rules, because special rules apply. Without it, people might assume every sandwich is between 1 and 9.

 Schwierigkeit: Bewertung: N/A Gelöst: 4 mal Beobachtet: 0 mal ID: 0003UJ

Lösungscode: