jasen Posted July 26, 2016 Report Share Posted July 26, 2016 (edited) There are 2 solutions, if we rule out Reflection Edited July 26, 2016 by jasen Quote Link to comment Share on other sites More sharing options...
0 Pickett Posted July 26, 2016 Report Share Posted July 26, 2016 Reveal hidden contents So reflections/rotations get a little strange with this because of the fact that you have stated that the middle-left and middle-middle squares can be a difference of 1. This means if you have a solution that works...and then reflect it across the Y-axis, there's a possibility that that reflected solution is not a valid solution anymore. Here's an example of this: This solution works with the original configuration: A=1, B=5, C=7, D=8, E=9, F=2, G=3, H=6, I=4 (G+H+I) = (A+B+C) =13 If I reflect that across the Y-axis...you get this (which is no longer valid because E/F have a difference one 1): A=7, B=5, C=1, D=2, E=9, F=8, G=4, H=6, I=3 (G+H+I) = (A+B+C) =13 With that being said, I could spend the time figuring out which ones are the true reflections/rotations/duplicates (some are easy to figure out) and which ones aren't...but here's all 24 of the possible solutions to the above: A=1, B=5, C=7, D=8, E=9, F=2, G=3, H=6, I=4 (G+H+I) = (A+B+C) =13 A=1, B=7, C=3, D=8, E=9, F=6, G=5, H=2, I=4 (G+H+I) = (A+B+C) =11 A=1, B=7, C=5, D=8, E=9, F=2, G=3, H=6, I=4 (G+H+I) = (A+B+C) =13 A=3, B=6, C=4, D=8, E=9, F=2, G=1, H=5, I=7 (G+H+I) = (A+B+C) =13 A=3, B=6, C=4, D=8, E=9, F=2, G=1, H=7, I=5 (G+H+I) = (A+B+C) =13 A=3, B=6, C=4, D=8, E=9, F=2, G=5, H=1, I=7 (G+H+I) = (A+B+C) =13 A=3, B=7, C=1, D=8, E=9, F=6, G=5, H=2, I=4 (G+H+I) = (A+B+C) =11 A=3, B=7, C=2, D=8, E=9, F=4, G=5, H=1, I=6 (G+H+I) = (A+B+C) =12 A=5, B=1, C=6, D=8, E=9, F=4, G=3, H=7, I=2 (G+H+I) = (A+B+C) =12 A=5, B=1, C=7, D=8, E=9, F=2, G=3, H=6, I=4 (G+H+I) = (A+B+C) =13 A=5, B=2, C=4, D=8, E=9, F=6, G=1, H=7, I=3 (G+H+I) = (A+B+C) =11 A=5, B=2, C=4, D=8, E=9, F=6, G=3, H=7, I=1 (G+H+I) = (A+B+C) =11 A=5, B=8, C=6, D=2, E=1, F=4, G=7, H=3, I=9 (G+H+I) = (A+B+C) =19 A=5, B=8, C=6, D=2, E=1, F=4, G=9, H=3, I=7 (G+H+I) = (A+B+C) =19 A=5, B=9, C=3, D=2, E=1, F=8, G=7, H=4, I=6 (G+H+I) = (A+B+C) =17 A=5, B=9, C=4, D=2, E=1, F=6, G=7, H=3, I=8 (G+H+I) = (A+B+C) =18 A=7, B=3, C=8, D=2, E=1, F=6, G=5, H=9, I=4 (G+H+I) = (A+B+C) =18 A=7, B=3, C=9, D=2, E=1, F=4, G=5, H=8, I=6 (G+H+I) = (A+B+C) =19 A=7, B=4, C=6, D=2, E=1, F=8, G=5, H=9, I=3 (G+H+I) = (A+B+C) =17 A=7, B=4, C=6, D=2, E=1, F=8, G=9, H=3, I=5 (G+H+I) = (A+B+C) =17 A=7, B=4, C=6, D=2, E=1, F=8, G=9, H=5, I=3 (G+H+I) = (A+B+C) =17 A=9, B=3, C=5, D=2, E=1, F=8, G=7, H=4, I=6 (G+H+I) = (A+B+C) =17 A=9, B=3, C=7, D=2, E=1, F=4, G=5, H=8, I=6 (G+H+I) = (A+B+C) =19 A=9, B=5, C=3, D=2, E=1, F=8, G=7, H=4, I=6 (G+H+I) = (A+B+C) =17 Quote Link to comment Share on other sites More sharing options...
0 Logophobic Posted July 26, 2016 Report Share Posted July 26, 2016 "the middle-middle square is adjacent to all other square" This implies that the restriction applies to diagonally adjacent squares. There are only two solutions, along with their vertical reflections, that qualify in this case. Quote Link to comment Share on other sites More sharing options...
0 jasen Posted July 27, 2016 Author Report Share Posted July 27, 2016 (edited) On 7/26/2016 at 12:50 PM, Pickett said: Reveal hidden contents So reflections/rotations get a little strange with this because of the fact that you have stated that the middle-left and middle-middle squares can be a difference of 1. This means if you have a solution that works...and then reflect it across the Y-axis, there's a possibility that that reflected solution is not a valid solution anymore. Here's an example of this: This solution works with the original configuration: ------ cut ---- Expand Some of your solutions is wrong, "adjacent" also means adjacent diagonally. Re filter your answers. Reflection works vertically Edited July 27, 2016 by jasen Quote Link to comment Share on other sites More sharing options...
1 Pickett Posted July 27, 2016 Report Share Posted July 27, 2016 On 7/27/2016 at 10:08 AM, jasen said: Some of your solutions is wrong, "adjacent" also means adjacent diagonally. Re filter your answers. Reflection works vertically Expand Ah, I missed a few of the diagonals (I accounted for the center square but not all): Reveal hidden contents 2 unique solutions, 1 reflection per solution (across the X-Axis) A=1, B=5, C=7, D=8, E=9, F=2, G=3, H=6, I=4 (G+H+I) = (A+B+C) =13 A=3, B=6, C=4, D=8, E=9, F=2, G=1, H=5, I=7 (G+H+I) = (A+B+C) =13 A=7, B=4, C=6, D=2, E=1, F=8, G=9, H=5, I=3 (G+H+I) = (A+B+C) =17 A=9, B=5, C=3, D=2, E=1, F=8, G=7, H=4, I=6 (G+H+I) = (A+B+C) =17 Quote Link to comment Share on other sites More sharing options...
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There are 2 solutions, if we rule out Reflection
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