Domino Castle Submissions pdf - Only the horizontal dominos marked, remaining are vertical.

Correctness of rules not checked (e.g. the one in page 11 is definitely invalid). If you notice any other grids missing rules, please post here.

22 submissions (out of which at least one is invalid)

I had the same problem.

One of the best contests ever. Congratulations for a fantastic set of puzzles. Spasiba Riad

Optimal Digital Ornament had most number of submissions.
The pdf is little tough to decrypt, but it is easy for those who have submitted the puzzle.
Riad probably has to spend lot of time checking this manually, so if you notice any errors / missing rules, please share.

My entry (110) has a typo. 2 cells transposed in the BL corner.

...If that cannot be allowed, could my previous 105 entry be considered?

I saw these two cells. It did not change your result (110).

Preliminary results have been published, I thank everyone for their participation and positive responses!

Congratulations to James (this is his second win in my contests), Tomoaki and Taro!

Once again thanks to Andrey Bogdanov, who tested all puzzles and translated them into English. And a special thanks to Deb Mohanty! He prepared pdfs with graphic solutions of optimization puzzles. It was a great pleasure holding contests with Deb .

Wow! I'm really pleased! I was hoping to do well, but was convinced I hadn't done _quite_ enough to win. Well done to Tomoaki and Taro also, Tomoaki in particular has beaten me in many optimising competitions over the years, and he wasn't far off again. :) (e.g. http://www.logic-masters.de/DOM/2009.php)
And this is the first time I've finished in the top 3 for any LMI test, so that's another personal milestone.

Big thanks to Riad, you are very clever at making new puzzle variations. Yes they are often hard, but we have a whole week to enjoy them and conquer their logic, which is a pleasant change from the other styles of 'speedy' competition. And the optimisers, well I struggled with those dominoes, it was early in the final morning when I finally found a solution that might be respectable...
And also thank you to Deb for the pdfs, it is great to see how others approached their solutions.

I guess some people might not have come across optimising puzzles before, so I thought I'd give a walkthrough for how I approached the Tetra-Sudoku puzzle. If someone else wants to discuss the other two, feel free.

I tried placing tetraminos in the grid, then filling them with small digits, but that did not go well. So then I chose a different approach. Also I reread the instructions, and noticed that I didn't have to use all 7 shapes!

It was recently proven that a solveable sudoku must have at least 17 clues, but there are thousands of ways to achieve that. So I started with a 17-clue sudoku like this:

..5 ... 46. 

1.. 27. ... 

8.. ... ... 

 

... ... ... 

... ... .12 

..3 .45 ... 

 

... ... ..1 

..4 ... ... 

.56 ..4 ...

The clues are spread out. I'm allowed to swap around rows and columns, as long as each 'group of 3' stays together. So I do this to try to bring the clues closer together, hopefully into groups of size 4.

... ... ... 

.3. .45 ... 

... ... .12 

 

... ... ..1 

.4. ... ... 

56. ..4 ... 

 

.5. ... 46. 

..1 27. ... 

..8 ... ...

Now I have the clues grouped into two full tetraminoes, and two groups of three, a pair, and a single. So 6 tetraminoes would cover all these clues. But I can't find a way to cover them all with only 5 tetraminoes.

Next I throw away that single 3. So I have a sudoku with 16 clues, and it has 1000+ solutions, but I can cover the remaining clues with 5 tetraminoes. And I can choose which 4 extra digits to add (two next to the 45, one beside the 121, and one joining the 4 to the 46)...
Now is when I also relabel the digits so that the most common (the 4s) become 1s, etc, to minimize the sum. So I'd like to add 4 more 'small' digits if I can.

... ... ... 

... .12 ... 

... ... .34 

 

... ... ..3 

.1. ... ... 

25. ..1 ... 

 

.2. ... 15. 

..3 47. ... 

..6 ... ...

If I add an 8 to R2C4 and an 8 to R7C6 then the grid is solveable except for a 2x2 square. This leads to a score of 69+4=73.

Or if I add a 6 to R2C4 and a 7 to R6C7 then again there is 2 solutions: all of the digits 1-7 can be placed, but there are no 8 or 9 clues to resolve where those go.

... ... ... 

... 612 ... 

... ... .34 

 

... ... ..3 

.1. ... ... 

25. ..1 7.. 

 

.2. ... 15. 

..3 47. ... 

..6 ... ...

I could add an 8-clue now, but going from 2 solutions to 1 solution only saves me 3 points, so I'd rather add a an 'unused' 1-clue and a 2-clue and stay with 2 solutions. After a final switch of columns 4 and 5 (so each shape is different), and another relabeling, this gives a score of 66+4=70.

... 2.. ... 

... 163 ... 

... ... .24 

 

... ... .12 

.1. ... ... 

35. ..1 7.. 

 

.3. ... 15. 

..2 74. ... 

..6 ... ...

(I hope those are readable, it's the only way I could think of to format a 9x9 sudoku grid)

Congratulations James for the top position and thanks for sharing your methodical approach for TetraSudoku.

I tried getting an answer with "randomly" starting with Tetrominoes with 1-2-3-4 and other small numbers. But could never got a score less than 100. (It looks like I am not the only one. I can see many Tetrominoes with 1234 in the pdf).