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3 x 3 table with constrains


jasen
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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If I reflect that across the Y-axis...you get this (which is no longer valid because E/F have a difference one 1):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    

 

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21 hours ago, Pickett said:
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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  ----

 

Some of your solutions is wrong, "adjacent" also means adjacent diagonally. Re filter your answers.

Reflection works vertically

Edited by jasen
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1 hour ago, jasen said:

Some of your solutions is wrong, "adjacent" also means adjacent diagonally. Re filter your answers.

Reflection works vertically

Ah, I missed a few of the diagonals (I accounted for the center square but not all):

Spoiler

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 

 

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