Matrix / math / Sudoku problem

[grango]

Hi,

I would need to complete the attached matrix, in a way, that the rows match with the total on the right and all the columns match with the total on the bottom. The gray parts should have no numbers and the green 1600 has to be calculated to the total of the column and row in question.

I've tried to solve this manually but can't get it right. Do you think there is a way to do this by some function like with the solver? If not, do you have any clue on how to solve this manually.

Thanks a load!

pic:
sieppaus1.JPG

[Glenn Kennedy]

How do you derive the 1600 from the values shown on your example? Also, can you attach the spread sheet, it'll be easier to work with.

[grango]

The 1600 is included in the total of 3924. For simplification you could take it completely away and subtract the sum from the total to get 2324.

Here you can find the spreadsheet:
https://www.dropbox.com/s/k3hwqoio581exet/Matrix1.xlsx

thanks!

[Glenn Kennedy]

I still don't understand what you are trying to do...

[grango]

Soo, have you ever played Sudoku? This is kinda like that. If you take the top row, the sum of these all cells should add up to 373. Then in the vertical way let's say the left most cells should add up to 373. So the values in the columns add up to the total in the bottom, and the values in the rows add up to the total on the right.

[Glenn Kennedy]

I prefer Kakuro (there's a good one every few days in The Guardian, (a UK paper http://www.theguardian.com/lifeandstyle/series/kakuro).

In answer to you Q... Solving this sort of request would be WAYYY beyond my abilities. If it's even possible...

Over to others!

[Crooza]

The way I read it there are 60 unknowns (cells where we don't know the value) and 18 equations (each row and each column is an equation). Now it also looks symmetrical around the diagonal so this would reduce the unknowns to 30 but it also reduces the number of unique equations to 9. To solve for x unknowns you need to have x unique equations. Therefore my take on this is that there is no one unique solution, but a number of solutions. Are there other constraints that we don't know about? Eg all numbers have to be integers, all numbers have to be positive, all numbers have to be between a certain range? If not I'd probably start filling more squares with zeros until I had 9 remaining unknowns and 9 equations.

From that point you can simply use matrix (array) formulas to solve for the unknown. Remembering that the inverse matrix multiplied by the result matrix will give you the solution. Minverse and mmult functions will be your friend here.