1) I borrowed from the answer in the linked Q&Alinked Q&A the fact that the total of all elements in the matrix will be 468.
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1) I borrowed from the answer in the linked Q&A the fact that the total of all elements in the matrix will be 468.
1) I borrowed from the answer in the linked Q&A the fact that the total of all elements in the matrix will be 468.
This means that the row and column rowssums are divisors of 468. Moreover, these sums have to be related to each other by a factor of 9/4 (or 4/9). With that information, I picked out the possible candidates for those sums out of the divisors of 468.
This means that the row and column rows are divisors of 468. Moreover, these sums have to be related to each other by a factor of 9/4 (or 4/9). With that information, I picked out the possible candidates for those sums out of the divisors of 468.
This means that the row and column sums are divisors of 468. Moreover, these sums have to be related to each other by a factor of 9/4 (or 4/9). With that information, I picked out the possible candidates for those sums out of the divisors of 468.
This is where I gave up for now, as even though the column and row lengths all add it to the correct values (52 for row, 117 for column), there are negative values. Moreover, there's no guarantee that the other values aside from C[1] to C[19] will be unique.
One idea for post-processing the reduced solution is to NestWhile with a different random samples of C[1] to C[19] until there are (1) no negative values, and (2) no repeating values, but I'd wasted enough time today working on this problem. Perhaps I could work on it some time later or someone else could arrive at the solution before then.
Lastly, the answer in the linked Q&A mentioned a backtracking algorithm to arrive at his/her solution. I'm not advanced enough to implement one in MMA so perhaps someone with knowledge in that area could think of a method to solve the problem.
This is where I gave up for now, as even though the column and row lengths all add it to the correct values (52 for row, 117 for column), there are negative values. Moreover, there's no guarantee that the other values aside from C[1] to C[19] will be unique. One idea for post-processing the reduced solution is to NestWhile with a different random samples of C[1] to C[19] until there are (1) no negative values, and (2) no repeating values, but I'd wasted enough time today working on this problem. Perhaps I could work on it some time later or someone else could arrive at the solution before then.
This is where I gave up for now, as even though the column and row lengths all add it to the correct values (52 for row, 117 for column), there are negative values. Moreover, there's no guarantee that the other values aside from C[1] to C[19] will be unique.
One idea for post-processing the reduced solution is to NestWhile with a different random samples of C[1] to C[19] until there are (1) no negative values, and (2) no repeating values, but I'd wasted enough time today working on this problem. Perhaps I could work on it some time later or someone else could arrive at the solution before then.
Lastly, the answer in the linked Q&A mentioned a backtracking algorithm to arrive at his/her solution. I'm not advanced enough to implement one in MMA so perhaps someone with knowledge in that area could think of a method to solve the problem.
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