## Ken's Puzzle of the WeekSums with 1 to 9

 1 2 4 2 22

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:
1. 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?
2. 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 -5
```5-1-9
- - -
3-2-6
- - -
7-4-8```
Sum of -3
```1+3-7
+ + -
5-2-6
- - -
9-8-4```
Sum of -1
```1+4-6
+ + -
7-3-5
- - -
9-8-2```
Sum of 1
```2+4-5
+ - -
7-9+3
- + -
8-6-1```
Sum of 3
```4+6-7
+ + -
8-2-3
- - -
9-5-1```
Sum of 5
```2-1+4
- - -
3-5+7
+ + +
6-9+8```
Sum of 11
```8-1+4
- + +
6+3+2
+ + +
9+7-5```
Sum 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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