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MeanDoku NC X 11 http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=13&t=1443 |
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Author: | Andrew [ Fri Aug 03, 2018 3:31 am ] |
Post subject: | MeanDoku NC X 11 |
In the MeanDoku thread HATMAN posted the link http://forum.enjoysudoku.com/post257549.html#p257549 This was for MeanDoku NC 2 but if you scroll down you will find MeanDoku NC X 11. Another good one for those new to MeanDoku NCs to try. It's also unusual in that each nonet has the maximum 12 coloured marks. Here is my walkthrough for MeanDoku NC X 11: Cells adjacent to green marks must total less than 10, blue must total 10, red must total more than 10. Also NC so horizontally/vertically adjacent cells cannot be {12}, {23}, … {78}, {89}, so at least one of the cells adjacent to each green mark must contain one of 1,2,3 as they cannot be {45}; similarly at least one of the cells adjacent to each red mark must contain one of 7,8,9 as they cannot be {56}. However since this appeared to be an easier puzzle I didn’t use that property; if I had my walkthrough would have been a bit shorter. This is a Killer-X. Prelims. Delete 9 from cells either side of green marks. Delete 5 from cells either side of blue marks. Delete 1 from cells either side of red marks. Clean-ups only as stated. 1. R1C1 = 1 (hidden single on D\, also for N1 but I spotted it on the diagonal first), no 2 in R1C2 + R2C1 (NC) 1a. R2C5 = 1 (hidden single in C5), no 2 in R13C5 + R2C46 (NC) 1b. R3C9 = 1 (hidden single in R3), no 2 in R24C9 + R3C8 (NC) 1c. R4C8 = 1 (hidden single in C8), no 2 in R4C7 + R5C8 (NC) 1d. R5C3 = 1 (hidden single in R5), no 2 in R46C3 + R5C24 (NC) 1e. R9C2 = 1 (hidden single in C2), no 2 in R8C2 + R9C13 (NC) 1f. R6C4 = 1 (hidden single in C4), no 2 in R6C5 + R7C4 (NC) 1g. R7C6 = 1 (hidden single in C6), no 2 in R68C6 + R7C57 (NC) 1h. R8C7 = 1 (hidden single in C7), no 2 in R8C8 + R9C7 (NC) 2. R9C9 = 9 (hidden single on D\, also for N9 but I spotted it on the diagonal first), no 8 in R8C9 + R9C8 (NC) 2a. R8C5 = 9 (hidden single in R8), no 8 in R79C5 + R8C46 (NC) 2b. R7C1 = 9 (hidden single in R7), no 8 in R68C1 + R7C2 (NC) 2c. R6C2 = 9 (hidden single in C2), no 8 in R5C2 + R6C3 (NC) 2d. R5C7 = 9 (hidden single in R5), no 8 in R46C7 + R5C68 (NC) 2e. R4C6 = 9 (hidden single in R4), no 8 in R3C6 + R4C5 (NC) 2f. R3C4 = 9 (hidden single in R3), no 8 in R24C4 + R3C35 (NC) 2g. R2C3 = 9 (hidden single in R2), no 8 in R1C3 + R2C2 (NC) 2h. R1C8 = 9 (hidden single in R1), no 8 in R1C79 + R2C8 (NC) Time for some clean-ups. Blue marks No 2 in R1C5 -> no 8 in R1C4 No 2 in R4C3 -> no 8 in R4C2 No 2 in R4C9 -> no 8 in R5C9 No 8 in R6C1 -> no 2 in R5C1 No 8 in R6C7 -> no 2 in R6C8 No 8 in R9C5 -> no 2 in R9C6 Green marks No 1 in R1C7 -> no 8 in R2C7 No 1,2 in R2C1 -> no 7 in R2C2 -> no 3 in R1C2 (blue) No 1 in R2C2 -> no 8 in R2C1 + R3C2 No 1,2 in R2C4 -> no 7 in R1C4 -> no 3 in R1C5 (blue) No 1 in R2C8 -> no 8 in R3C8 No 1,2 in R3C5 -> no 7 in R3C6 -> no 3 in R2C6 (blue) No 1,2 in R3C8 -> no 7 in R2C8 -> no 3 in R2C9 (blue) No 1 in R4C2 -> no 8 in R4C1 No 1 in R4C5 -> no 8 in R5C5 No 1,2 in R5C2 -> no 7 in R4C2 -> no 3 in R4C3 (blue) No 1 in R5C6 -> no 8 in R6C6 No 1,2 in R5C8 -> no 7 in R5C9 -> no 3 in R4C9 (blue) No 1 in R5C9 -> no 8 in R6C9 No 1,2 in R6C6 -> no 7 in R5C6 No 1 in R7C2 -> no 8 in R7C3 No 1 in R7C3 -> no 8 in R8C3 No 1 in R7C89 -> no 8 in R7C89 No 1 in R8C1 -> no 8 in R9C1 No 1 in R8C4 -> no 8 in R9C4 No 1,2 in R9C1 -> no 7 in R8C1 -> no 3 in R8C2 (blue) No 1,2 in R9C7 -> no 7 in R9C8 -> no 3 in R8C8 (blue) No 1 in R9C8 -> no 8 in R9C7 Red marks No 9 in R1C2 -> no 2 in R1C3 No 9 in R1C5 -> no 2 in R1C6 No 8,9 in R2C1 -> no 2,3 in R3C1 No 8,9 in R2C7 -> no 2,3 in R3C7 No 9 in R2C9 -> no 2 in R1C9 No 9 in R3C1 -> no 2 in R3C2 -> no 7 in R3C3 (green) No 9 in R3C7 -> no 2 in R2C7 -> no 7 in R1C7 (green) No 8,9 in R4C1 -> no 3 in R5C1 -> no 7 in R6C1 (blue) No 8,9 in R4C4 -> no 3 in R5C4 No 9 in R5C1 -> no 2 in R4C1 No 9 in R5C4 -> no 2 in R4C4 + R5C5 -> no 7 in R4C5 (green) No 8,9 in R5C8 -> no 3 in R6C8 -> no 7 in R6C7 (blue) No 8,9 in R6C6 -> no 3 in R6C5 No 9 in R6C8 -> no 2 in R6C9 No 8,9 in R7C5 -> no 3 in R7C4 -> no 7 in R8C4 (blue) No 9 in R7C7 -> no 2 in R7C8 -> no 7 in R7C9 (green) No 8,9 in R7C8 -> no 3 in R7C7 No 9 in R8C2 -> no 2 in R7C2 + R8C3 -> no 7 in R7C3 (green) No 8,9 in R8C3 -> no 3 in R9C3 No 8,9 in R8C6 -> no 3 in R9C6 -> no 7 in R9C5 (blue) No 9 in R8C8 -> no 2 in R8C9 3a. 2 in N5 only in R4C5 + R5C6, no 3 in R5C5 (NC) 3b. 8 in N5 only in R5C4 + R6C5, no 7 in R5C5 (NC) 3c. R5C5 = {456} -> no 4,5,6 in R5C4 + R6C5 (red + NC) 3d. Naked pair {78} in R5C4 + R6C5, locked for N5, no 6 in R5C5 (NC) 3e. R5C5 = {456} -> no 4,5,6 in R4C5 + R5C6 (green + NC) 3f. Naked pair {23} in R4C5 + R5C6, locked for N5, no 4 in R5C4 (NC) 3g. R5C5 = 5, placed for both diagonals 3h. Naked pair {46} in R4C4 + R6C6, locked for D\ Clean-up: no 4,6 in R1C2 + R9C8 (blue) 3i. Naked pair {23} in R2C2 + R3C3, locked for N1, no 4 in R3C2 (NC) 3j. R1C2 = {78} -> no 7 in R1C3 (NC) 3k. Naked pair {78} in R7C7 + R8C8, locked for N9, no 6 in R7C8 (NC) 3l. 8 in N7 only in R8C2 + R9C3, no 7 in R8C3 (NC) 3m. R8C3 = {3456} -> no 4,5,6 in R8C2 + R9C3 (red + NC) 3n. Naked pair {78} in R8C2 + R9C3, locked for N7, no 6 in R8C3 (NC) Clean-up: no 4,6 in R8C1 (blue) 3o. R9C3 = {78} -> no 7 in R9C4 (NC) 3p. 5 in N7 only in R7C2 + R8C3, no 4,6 in R7C3 (NC) 3q. Naked pair {23} in R7C3 + R8C2, locked for N7 3r. Naked pair {23} in R37C3, locked for C3 3s. Naked pair {78} in R18C2, locked for C2 3t. R8C3 = {45} -> no 4 in R8C4 (NC) Clean-up: no 6 in R7C4 (blue) 3u. R3C2 = {56} -> no 4,5,6 in R3C1 (red + NC) 3v. Naked pair {78} in R1C2 + R3C1, locked for N1 3w. R3C1 = {78}, no 7 in R4C1 (NC) 3x. R35C1 = {78} (hidden pair in C1), no 6 in R4C1 (NC) Clean-up: no 4,6 in R6C1 (blue) 3y. Naked pair {23} in R68C1, locked for C1 3z. R4C1 = {45} -> no 4,6 in R4C2 (green + NC) Clean-up: no 4,6 in R4C3 (blue) 3aa. Naked pair {23} in R4C2 + R6C1, locked for N4 3ab. Naked pair {78} in R4C3 + R5C1, locked for N4 3ac. Naked pair {23} in R4C25, locked for R4 4a. 2 in N2 only in R1C45 = [28] (blue) or R23C6 = [82] (blue), 8 in R1C5 + R2C6, locked for N2, no 7 in R1C6 (NC) 4b. R1C6 = {3456} -> no 4,6 in R1C5 + R2C6 (red + NC) Clean-up: no 4,6 in R1C4 + R3C6 (blue) 4c. Naked pair {23} in R1C4 + R3C6, locked for N2 4d. Naked pair {78} in R1C5 + R2C6, locked for N2, no 6 in R1C6 (NC) 4e. R1C6 = {45} -> no 4,5 in R1C7 (NC) 4f. R2C6 = {78} -> no 7 in R2C7 (NC) 4g. R2C7 = {3456} -> no 4,6 in R3C7 (red + NC) 4h. R3C7 = {78} -> no 7 in R3C8 + R4C7 (NC) 4i. Naked pair {78} in R3C7 and R8C2, locked for D/ 4j. R2C9 + R3C7 = {78} (hidden pair in N3) Clean-up: no 4,6 in R2C8 (blue) 4k. Naked pair {23} in R2C8 + R7C3, locked for D/ 4l. R2C8 = {23} -> no 3 in R2C7 + R3C8 (NC) 4m. R1C7 + R2C8 = {23} (hidden pair in N3), no 4 in R2C7 (NC) 5a. R4C39 = {78} (hidden pair in R4) Clean-up: no 4,6 in R5C9 (blue) 5b. Naked pair {78} in R24C9, locked for C9 5c. R6C9 = {3456} -> no 4,6 in R6C8 (red + NC) Clean-up: no 4,6 in R6C7 5d. Naked pair {23} in R5C9 + R6C7, locked for N6 5e. Naked pair {78} in R4C9 + R6C8, locked for N6 5f. Naked pair {23} in R16C7, locked for C7 5g. Naked pair {23} in R29C8, locked for C8 5h. R7C8 = {45} -> no 4,5,6 in R7C9 (green + NC) 5i. Naked pair {23} in R7C9 + R9C8, locked for N9 5j. Naked pair {23} in R57C9, no 4 in R6C9 (NC) 5k. R57C4 = {78} (hidden pair in C4), no 7 in R7C5 (NC) Clean-up: no 6 in R8C4 (blue) 5l. R9C36 = {78} (hidden pair in R9), no 7 in R8C6 (NC) Clean-up: no 4,6 in R9C5 (blue) 5m. Naked pair {23} in R8C4 + R9C5, locked for N8, no 4 in R9C4 (NC) 5n. Naked pair {78} in R7C4 + R9C6, locked for N8 [Now some short forcing chains to place the remaining 5s.] 6a. R1C4 = 2 => R1C7 = 3, no 4 in R1C6 (NC) or R1C4 = 3, R1C7 = 2, R2C8 = 3 => R2C9 = 7 (blue), no 6 in R1C9 (NC) => R1C9 = 4 -> R1C6 = 5 6b. R9C4 = 5 (hidden single in C4) 6c. R4C3 = 7 => R4C2 = 3 (blue), no 4 in R4C1 or R4C3 = 8, R5C1 = 7, no 6 in R5C2 (NC) => R5C2 = 4 -> R4C1 = 5 6d. R6C9 = 5 (hidden single in R6) 6e. R2C7 = 5 (hidden single in R2) 6f. R3C2 = 5 (hidden single in R3) 6g. R7C8 = 5 (hidden single in R7) 6h. R8C3 = 5 (hidden single in R8) Then working through the options starting from one of the {23} cells and applying NC leads to two possible solutions. As HATMAN said, there are two solutions, but that doesn't spoil this puzzle: 1 7 4 2 8 5 3 9 6 6 3 9 4 1 7 5 2 8 8 5 2 9 6 3 7 4 1 5 2 8 6 3 9 4 1 7 7 4 1 8 5 2 9 6 3 3 9 6 1 7 4 2 8 5 9 6 3 7 4 1 8 5 2 2 8 5 3 9 6 1 7 4 4 1 7 5 2 8 6 3 9 and 1 8 6 3 7 5 2 9 4 4 2 9 6 1 8 5 3 7 7 5 3 9 4 2 8 6 1 5 3 7 4 2 9 6 1 8 8 6 1 7 5 3 9 4 2 2 9 4 1 8 6 3 7 5 9 4 2 8 6 1 7 5 3 3 7 5 2 9 4 1 8 6 6 1 8 5 3 7 4 2 9 With hindsight I spotted: With the symmetry of the placements of 1 and 9, it’s hardly surprising that R5C5 = 5. It was only after I’d finished the puzzle that I noticed the complete symmetry and checked the symmetry of the blue marks, and the corresponding pairs of green and red marks. This is similar to symmetry which has appeared in a few Assassins in the Killer forum. If corresponding cells, cages in the case of killers, or marks in the case of MeanDoku NCs, are all complimentary about the centre of the puzzle, then it is symmetrical. In this puzzle each of the pairs of blue marks, for example in R1C45 and R9C56, are symmetrical about R5C5. Similarly each green mark has a red mark in the corresponding position, for example green in R1C12 and red in R9C89. With total symmetry it follows that R5C5 must be 5, which could be used as a shortcut. |
Author: | HATMAN [ Fri Aug 24, 2018 10:30 am ] |
Post subject: | Re: MeanDoku NC X 11 |
Hi Andrew To my memory I did not notice the symmetry. Well noted. Maurice |
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