Unique dominos and quadruplets
(Published on 5. January 2021, 22:06 by PetLov)
I was trying to figure out how to avoid too much colorful dots in the puzzle and this is what came out from that process.
No repeated totals gives no repeated colors.
Hope you enjoy the puzzle. Any comments and/or ratings are highly appreciated.
The following Sudoku Grid must be filled with the digits 1 to 9 in such a way that every row, column and box contains each digit exactly once.
In addition, the grid contains a number of circles. Every circle is at the center of a Domino or a Square-Tetromino. The sum of the digits around a circle can not be equal to the sum of the digits around another circle.
There are three special numbers 1, 5, and 9, called Key digits.
Circles can contain clues about the digits surrounding the circle based on the following rules:
1) If two or more Key digits surround a circle, then the circle must be empty.
2) If exactly one Key digit surrounds a circle, then that Key digit will be displayed.
3) If no Key digit surrounds a circle, then the highest digit surrounding a circle will be displayed.
4) Some of the information has been omitted and replaced by a "?" which has to be deduced by the solver. A "?" can stand for any digit or the empty character.
Hint 1: How many different sums can you make with 2 and 4 digits?
Hint 2: How many dominos are there in the grid that all have to add to a different sum?
Example:
Solution code: Row 7 and column 3
Comments
on 8. January 2021, 13:47 by PetLov
Clarifying rules.
Thank you Narayana.
on 8. January 2021, 08:06 by Narayana
I see a couple of complaints about the explanation of the rules on the hidden comments...
[One a bit rude TBH...]. Perhaps that is why this super nice puzzle does not have more solves, which is a pity!
Here is my attempt at clarifying the rules, including html formatting for nice display. PetLov, feel free to just copy paste this if you think my explanation is useful.
<p>The following Sudoku Grid must be filled with the digits 1 to 9 in such a way that every row, column and box contains each digit exactly once. </p>
<p>In addition, the grid contains a number of <b>circles</b>. Every circle is at the center of a Domino or a Square-Tetromino. The <b>sum</b> of the digits around a circle can <b>not</b> be equal to the sum of the digits around another circle.</p>
<p>There are three special numbers 1, 5, and 9, called <b>Key</b> digits. </p>
<p>Circles can contain <b>clues</b> about the digits surrounding the circle based on the following rules:<br>
1) If two or more Key digits surround a circle, then the circle must be <b>empty</b>.<br>
2) If exactly one Key digit surrounds a circle, then that <b>Key digit</b> will be displayed.<br>
3) If no Key digit surrounds a circle, then the <b>highest</b> digit surrounding a circle will be displayed.<br>
4) Some of the information has been omitted and replaced by a "?" which has to be deduced by the solver. A "?" can stand for any digit or the empty character.
</p>
*** Thank you so much Narayana. I will make the change. However, the puzzle is lost in the flood now. The flood I'm contributing to ironically enough :-)
on 8. January 2021, 03:01 by cdwg2000
Very beautiful design, pleasant logical process, highly recommended! Thank you the author for the clarification and supplementary explanation of the rules!
on 7. January 2021, 20:48 by PetLov
Added image with examples.
Hope this helps.
on 7. January 2021, 08:36 by PetLov
Clarification of the rules and added hints.
