[SPOILER] Solution to Puzzle

[Aloysius]

I think others have already posted potential solutions to the math puzzle using computer programs, but for those who want a more organic approach I solved it without a computer.

 

 

  Your goal is to make a grid, well two, in which all the columns, rows, and diagonals add to 15. The position of a number in grid A must be different than the position of that number in grid B except for the center value.  I made the assumption that each of the two grids would use only the numbers 1-9 once and that the middle number would be the same (why else include the caveat?).

 

 

I ascribed a variable for each of the nine positions in the grid, A-I, starting in the top left and going top to bottom. You know from the setup that each row (e.g. A+B+C) = 15 and that therefore all the values combined must equal 45. If you use these to make a few equations you can determine that A+I = G+C and that D-H = B-F (assuming you use absolute value). With a few grids meeting this requirement I determined that the value of the interior (i.e. B + D + F + H) and the corners (A + C + G + I) is determined by the center value, E. Only one center value creates a grid of 45 - when E = 5. Using the equations and this center value I created one grid which I then slightly modified to create the second.

 

 

 

492     618

357     753
816     294

 

 

I haven't tried it yet in game, so I don't know what the reward is. But bravo on an amazingly difficult puzzle! This took me hours!  

[Lucky98]

Spoiler

The way I did it was by simply listing out all the possible sums of three numbers between 1-9 that added up to 15, and tried assigning them to a grid via trial and error. I also knew that the numbers 7, 8, and 9 couldn't be in the same column, row, or diagonal, so that limited positions.

 

took me about 10-15 minutes lol  Actually solving the in game puzzle took me a while though

 

[Aloysius]

1 hour ago, Lucky98 said:

  Reveal hidden contents

The way I did it was by simply listing out all the possible sums of three numbers between 1-9 that added up to 15, and tried assigning them to a grid via trial and error. I also knew that the numbers 7, 8, and 9 couldn't be in the same column, row, or diagonal, so that limited positions.

 

took me about 10-15 minutes lol  Actually solving the in game puzzle took me a while though

 

I thought of doing something similar, making little cut out dominoes of each combination that equaled 15.

[wcv]

5 hours ago, Aloysius said:

I think others have already posted potential solutions to the math puzzle using computer programs, but for those who want a more organic approach I solved it without a computer.

 

  Reveal hidden contents

  Your goal is to make a grid, well two, in which all the columns, rows, and diagonals add to 15. The position of a number in grid A must be different than the position of that number in grid B except for the center value.  I made the assumption that each of the two grids would use only the numbers 1-9 once and that the middle number would be the same (why else include the caveat?).

 

 

I ascribed a variable for each of the nine positions in the grid, A-I, starting in the top left and going top to bottom. You know from the setup that each row (e.g. A+B+C) = 15 and that therefore all the values combined must equal 45. If you use these to make a few equations you can determine that A+I = G+C and that D-H = B-F (assuming you use absolute value). With a few grids meeting this requirement I determined that the value of the interior (i.e. B + D + F + H) and the corners (A + C + G + I) is determined by the center value, E. Only one center value creates a grid of 45 - when E = 5. Using the equations and this center value I created one grid which I then slightly modified to create the second.

 

 

  Hide contents

492     618

357     753
816     294

 

 

I haven't tried it yet in game, so I don't know what the reward is. But bravo on an amazingly difficult puzzle! This took me hours!  

Spoiler

Bravo on solving it mathematically. Its a magic square. Putting the numbers in is harder than actually finding the solution though.

 

[Aloysius]

2 hours ago, wcv said:

  Reveal hidden contents

Bravo on solving it mathematically. Its a magic square. Putting the numbers in is harder than actually finding the solution though.

 

Yeah I am finding that out! Do you have any tips? I know it starts with the numbers in the same place each time, but I can't figure out an easy way to move them to where they need to be.

[wcv]

Spoiler

Focus on doing either one row or column at a time, starting from either the top if you start with rows as I did, or from the left if using columns. When you complete the first row or column keep it intact as you keep moving things around. So let's say the first row is going to be 249 and the second is going to be 753 (this was mine) I lined up the 249 first I then got the seven into the correct row and moved it into position. Then I used the third row to move the 5 and 7 into place (adjusting as necessary to keep them in the right spot.

 

One point that might be missed when solving it is, when you are done messing with the row/column that you need to move immediately you should shift the solved bits back into place so they don't get too mixed up.

 

Be patient and take your time as well. If you rush then the numbers already solved can easily get scrambled again, leaving you having to restart.

 

Once you have the flow of the movements down it gets significantly easier even though moving the numbers themselves gets more complicated.