the clock has stopped submissions again

Wow, lots of entries, and lots of great optimizer submissions.
Congratulations to those that found the optimal answers, and a big thank you to Riad and LMI for a fun and successful contest. :)

I will share my observations from optimization puzzles. Maybe someone will find it interesting :)


Problem #10

Maximizing N, the number of streets, is the same for both approaches (including or excluding the absence of 2x2 white areas as a rule of Town puzzle).
Observation 1. N <= 18. The proof is by checking how streets may be distributed and checking some cases. I will just give a sketch without technical details. It is quite intuitive but formal details are very long. So there are at most 12 dark rectangles in the grid (at most 4 rectangles in one row and at most 3 rectangles in one column). Hence, all horizontal streets must touch (from above or below) the rectangle which "touches" an upper or lower border of the grid (I say that the rectangle touches a border when it is at most 1 cell apart from the border). From that you can deduce that there are at most 12 horizontal streets and how they may be distributed. Similarly, there are at most 12 vertical streets. Analysing the distribution, some of them cannot occur together or they must be "glued" together. Here comes checking some cases and after that you obtain 2 limit cases. One with 3 vertical streets coming through the whole grid (but then easily it comes that there are at most 17 streets) and one with 2 long horizontal streets (there are at most 6 horizontal and 12 vertical streets). And this is our case. All eight middle rows are determined here. After that, by distributing streets over the upper and lower row, we are getting 5 different solutions (accurate to symmetry).

Observation 2. (including the absence of 2x2 white areas as a rule of Town puzzle) When N = 18, the sum of given values >= 26. The proof is by drawing 5 possible patterns and modifying them by some small changes. If you find another solution which differs only at e.g. row #1, column #1 and column #2, then you know that you must use at least one of these values. After that you get some sets of rows or columns from which you must use at least one. And actually we are getting a few disjoint sets so the number of cases is really limited here. Finally, there are exactly 2 different solutions accurate to symmetry (4 different solutions generally) meeting (N, sum) = (18, 26).
The same method works for the second aproach without the rule of white areas. I did not check it but I think that there are a few times more cases to analyse to get the most optimal solution but still I think it can be done with a pencil and rubber during the contest.


Problem #11

I do not have any formal observation here. I came here with 36 diamonds and area = 143 but maybe it can be done better. How did I get it? There are so many cases that I must have decided for some assumptions. We want to get as most as we can common diamonds. Cards #10, #9, #8, #7 have the most number diamonds so I just checked many ways of joining them together. When these cards had totally <= 25 diamonds, I was trying to join next cards (#6, #5, #4, #3, #2) consecutively in the best possible way locally.


Problem #12

Firstly it is provable that you cannot obtain the value of 60. It is because there are no 2 disjoint distributions of full flotilla. Hence, the value of 59 is the greatest. When I found one, I did not analyse this problem any longer. But I obtained it by drawing the random set of full flotilla as fragments of the sea (all horizontal fragments - of length 4 and 2 in the first row, of length 3 and 3 in the second row, of length 2 and 2 and 1 in the fifth row, of length 1 and 1 and 1 in the seventh row). I checked it. It didn't work but I noticed that moving two 1-cell elements from the seventh row to the right side is enough to fix it. So the way how I did it makes me believe that there are at least hundreds of solutions with that value. Also there are 8 different submissions with that value :)


Edited by lukasz6500 2020-04-19 8:35 PM

Preliminary results will be published in the next few minutes. We decided not to include points for problem 10 in the final table. The reason is the complexity or ambiguity in the rules, and from a fairness perspective.

Because flash problems I did not submited my solutions, but I really enjoyed problems. Thanks.

Riad, thank you so much for putting this together! I loved the puzzles and had a lot of fun working on them. Build a Dominoes and Diatapa were my favorites. Thank you!

Thank you Walker, thanks to all participants!

Congratulations to Lukasz, Hugo and Tomoya!

Riad! Thank you for the most powerful and interesting contest! This year was a lot of fun! It’s fun because this contest showed that we are all people, not just machines that create and solve puzzles!

Riad Thanks a lot for this contest which is the "Paris-Roubaix" of puzzle, the most enduring contest of the year. a monument. a classical event. Glad that the number of participants is increasing showing thesuccess of the event. Already looking forward for next year

This is my first time to join this contest series and I really love it, so thank you very much Riad for the puzzles! :D

Btw, I really like (9) CHAIN BETWEEN POLYOMINOES, then (5) BUILD A DOMINOES comes next.

One suggestion maybe: For an answer format involving the number of turns, especially (8) BUILD A HEXMAZE, it is easy to miscount the number. I have to recount like 5 times until I'm sure that the answer is 101 instead of 100 (3 times I counted 100, and only 2 times I counted 101.) Maybe the answer format can be simpler and easier like the content/wall of some rows, or the total number of turns (not just obtuse one.)

Edited by athin 2020-04-20 5:09 AM

Congratulations to Lukasz Kalinowski, Hugo van Rooijen and Tomoya Kimura for taking the top three places.

Thanks to the 112 participants from 31 countries. The participation was much higher compared to 2019. 36 participants completed the first 9 puzzles, and 24 participants scored points in the Optimzers. The median score of the test was 47. Italy had 14 participants, India 12, USA and France had 11 participants each.

Puzzle #1 (Battleships with Losses) was solved by the highest number of participants (96). Puzzles #8 (Build a Hex Maze) and #9 (Chain between Polyominoes) were each solved by 62 participants, the least among the first 9 puzzles.

Thanks Riad for the engaging puzzles!

And, thanks to all participants for healthy discussions, suggestions and constructive criticisms!

Thanks Riad for the great competition and wonderful puzzles! I admire both logic and beauty of all of them. You do an amazing job every year! Btw, may I write some emotional shit? Yolo, let's do it! I have been struggling with a major depression, anxiety problems and drug abuse for a long time. And it is not only a fight against stigmatization which is a serious problem here where I live. First of all, it is a fight against myself - my low self-esteem, lack of self-confidence and emotions. I do not usually care about results but I must admit that this time is a little bit different. When you are hitting the bottom, every little or bigger thing, which increases your confidence, makes you feel that you can get back to life. It is still going to be a tough road ahead but let it be a good point to go through it :)

And also, thanks to all people who helped preparing the competition and to all participants. Congratulations to all of you and see you somewhere in the world :) Thanks!

Thanks Riad! And Lukasz, all the best. Congrats on your win :)

Really enjoyed Riad .... The solutions Booklet please.

If there are many to count, I usually number them writing small numbers in fields. It's my answer to Athin

Edited by sladjana 2020-04-20 4:20 PM

Is there a solution book --- I really like these puzzles..... I got stuck on the dominoes..... I want to see how close I am and I am not sure if all the dominoes have to be interconnected ?/