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Place all of the digits 1-9 into the white boxes and one of the symbols (+ or -) into each of the gray boxes such that:

- Each of the six rows and columns have the same sum (other than 15). There's definitely a solution with a common sum of 5. Are there others?
- The sum of each row or column is equal to the noted number in its first square. For example, the third column will have a sum of 4, and the first row and column will both have a sum of 1.

Source: Original. [Thanks to Mark Rickert for updating part 2 to a solvable problem.]

Solutions were received from Mark Rickert, Kirk Bresniker, Bernie Erickson, Susil Kumar Jena and Claudio Baiocchi.

Part 1 has solutions for sums: -5,-3,-1, 1,3,5,11,13. Here's an example of each:

Sum of -55-1-9 - - - 3-2-6 - - - 7-4-8Sum of -3

1+3-7 + + - 5-2-6 - - - 9-8-4Sum of -1

1+4-6 + + - 7-3-5 - - - 9-8-2Sum of 1

2+4-5 + - - 7-9+3 - + - 8-6-1Sum of 3

4+6-7 + + - 8-2-3 - - - 9-5-1Sum of 5

2-1+4 - - - 3-5+7 + + + 6-9+8Sum of 11

8-1+4 - + + 6+3+2 + + + 9+7-5Sum of 13

7-2+8 - + + 3+6+4 + + + 9+5-1

Part 2 has one solution:

4-1-2 + - - 6-7+3 - + + 9+8+5

Claudio Baiocchi extended part 1 to look for diagonal solutions as well, finding a solution to a previous problem on this site.

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