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NC Repeat X 3 H http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=13&t=1391 |
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Author: | Andrew [ Mon Oct 24, 2016 10:39 pm ] |
Post subject: | Re: NC Repeat X 3 H |
Thanks HATMAN for another interesting puzzle. Not sure why part of the instructions was in small type; that part made it clearer and didn't give anything away. Maybe I missed something but I found it quite hard, definitely Assassin level. I used several forcing chains; I would expect that using contradictions would be similarly hard. Second time through, while checking my walkthrough, I managed to find some simplifications. Thanks HATMAN for pointing out that I’d carelessly included {167167} in the possible combinations for the 28(6) double cage. I’ve changed step 1c without that combination. Here is my walkthrough: |
Author: | HATMAN [ Thu Nov 03, 2016 5:03 am ] |
Post subject: | Re: NC Repeat X 3 H |
I noticed from Andrew's solution that 6 is forced in R456c5 my approach had been an unsatisfactory multicase one this reduced it to an (in my view) acceptable multicase one, so: Non-consecutive (NC), killer-X. The cages are maximum repeat so: XYZ-XYZ or TU-U. Prelims a) 22(3) cage at R3C3 = 9{49}/8{68}/7{87}, 7/8/9 & no 1,2,3,5 b) 22(6) double cage at R3C4, 11(3)*2 = {137137/146146} (cannot be {128128/236236/245245} because of double-row NC), no 2,5,8,9 c) 26(6) double cage at R4C3, 13(3)*2 = {139139/148148/157157/247247} (cannot be {238238/256256/346346} because of double-row NC), no 6 d) 28(6) double cage at R4C6, 14(3)*2 = {149149/158158/248248/257257} (cannot be {167167/239239/347347/356356} because of double-row NC), no 3,6 e) The blank double cage at R6C4 cannot contain consecutive numbers because of double-row NC (this is the fundamental concept for the design of the puzzle and why I used small letters) 1a. 22(6) double cage at R3C4 = {137137/146146}, 1 locked for R34 + N25 1b. 6 not in 26(6) double cage at R4C3 or 28(6) double cage at R4C6, r456c5 = 45-1/2*26 - 1/2*28 = 18(3) = {369} not {678} = 3{69}/6{39} 1c. 11(3) @r4c456 = [137/731/164/461] 1d. N5:13(3) = {148/157/247} = 1{48}/1{57}/4{27}/7{24} 1e. N5:14(3) = {158/248/257} = 1{58}/4{28}/7{25} 2 there are four cases for the 11(3) at r4c4 2a. case [137]: 14(3) = 7{25}; 13(3) = 1{48} 2b. case [731]: 14(3) = 1{58}; 13(3) = 7{24} 2c. case [461]: 14(3) = 1{58}; 13(3) = 4{27} 2d. case [164]: 14(3) = 4{28}; 13(3) = 1{57} Consider the case combinations allowing for NC 3 case [137]: r56c4,5,6 = {48}{69}{25} 3a. r5 = 495, r6 = 862 22(3) fail on 9 at r5c5 and {148} r4c3 3b. r5 = 862, r6 = 495 fail (cage at r6c4) 4 case [731]: r56c4,5,6 = {24}{69}{58} 4a. r5 = 268, r6 = 495 fail (cage at r6c4) 4b. r5 = 295, r6 = 468 fail 798 on d\ clash r3c3 4c. r5 = 468, r6 = 295 22(3) fail [68] at r5c56 and {247} r4c3 4c. r5 = 495, r6 = 268 fail 798 on d\ clash r3c3 5 case [461]: r56c4,5,6 = {27}{39}{58} 22(3) = [886], r6c6 = 5, r5c6 = 8, r5c5 = 3, r5c4 = 7, r6c4 = 2, r6c5 = 9 fail N4 no room for 5 6 case [164]: r56c4,5,6 = {57}{39}{28} 6a. r5 = 592, r6 = 738 fail (cage at r6c4) 6b. r5 = 792, r6 = 538 fail D\ 98 r3c4 and {157} clash r3c3 6c. r5 = 538, r6 = 792 OK so far 6d. r5 = 738, r6 = 592 OK So far 7 N5: c4 =1{57}, c5 = [639], c6 = [ 482] 8 NC on 89 at r3c3, r4c2 8a. N4 HS r4c2 = 9 22(3) = [994] Singles and simple NC from here Difficulty: nothing very hard for NC and the set of cases reasonable so difficulty less than 1.0. How many cases is acceptable I wonder? My original 48 is in my view not acceptable. Of course it is not just the number it is the shortness of the elimination in each case, but most of mine died very easily and a couple died easily enough. I often post puzzles where I have a solution which I do not consider acceptable - I cannot remember a case where someone did not come up with an acceptable one. |
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