@ 2013-04-16 4:29 AM (#10641 - in reply to #10427) (#10641) Top | |
Posts: 187 Country : New Zealand | kiwijam posted @ 2013-04-16 4:29 AM 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. |
@ 2013-04-16 6:27 AM (#10642 - in reply to #10641) (#10642) Top | |
Posts: 187 Country : New Zealand | kiwijam posted @ 2013-04-16 6:27 AM 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. 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. ... ... ... 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. ... ... ... 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. ... ... ... 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.. ... (I hope those are readable, it's the only way I could think of to format a 9x9 sudoku grid) |
@ 2013-04-16 11:03 AM (#10645 - in reply to #10427) (#10645) Top | |
Country : India | debmohanty posted @ 2013-04-16 11:03 AM 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). |