In this puzzle, each empty square needs to be filled in with a positive integer.
Each string of adjacent squares needs to form an arithmetic sequence.
A horizontal string of squares increases from left to right.
A vertical string of squares increases from top to bottom.
+--+--+--+--+--+
| | | |13| |
+--+--+--+--+--+--+--+
| |XXXXXXXX| |39| |
+--+XXXXXXXX+--+--+--+
| |XXXXXXXX|44|XX| |
+--+XXXXX+--+--+--+--+
|31|XXXXX| | | | |
+--+--+--+--+--+--+--+--+
| | | | | |XXXXX| |
+--+--+--+--+--+XXXXX+--+
|35|XXXXXXXX| |XXXXX| |
+--+XXXXXXXX+--+--+--+--+
| |XXXXXXXX| |78| | |
+--+--+--+--+--+--+--+--+
| |49| | | |
+--+--+--+--+--+
This is an original problem.
+----+----+----+----+----+
| | | | | |
| 4 | 7 | 10 | 13 | 16 |
| | | | | |
+----+----+----+----+----+----+----+
| |XXXX|XXXX|XXXX| | | |
| 13 |XXXX|XXXX|XXXX| 30 | 39 | 48 |
| |XXXX|XXXX|XXXX| | | |
+----+----+----+----+----+----+----+
| |XXXX|XXXX|XXXX| |XXXX| |
| 22 |XXXX|XXXX|XXXX| 44 |XXXX| 56 |
| |XXXX|XXXX|XXXX| |XXXX| |
+----+----+----+----+----+----+----+
| |XXXX|XXXX| | | | |
| 31 |XXXX|XXXX| 55 | 58 | 61 | 64 |
| |XXXX|XXXX| | | | |
+----+----+----+----+----+----+----+----+
| | | | | |XXXX|XXXX| |
| 33 | 40 | 47 | 54 | 61 |XXXX|XXXX| 72 |
| | | | | |XXXX|XXXX| |
+----+----+----+----+----+----+----+----+
| |XXXX|XXXX|XXXX| |XXXX|XXXX| |
| 35 |XXXX|XXXX|XXXX| 67 |XXXX|XXXX| 80 |
| |XXXX|XXXX|XXXX| |XXXX|XXXX| |
+----+----+----+----+----+----+----+----+
| |XXXX|XXXX|XXXX| | | | |
| 37 |XXXX|XXXX|XXXX| 73 | 78 | 83 | 88 |
| |XXXX|XXXX|XXXX| | | | |
+----+----+----+----+----+----+----+----+
| | | | | |
| 39 | 49 | 59 | 69 | 79 |
| | | | | |
+----+----+----+----+----+
If anyone's interested, I used Excel and played around a little... there're only "two degrees of freedom" here...
For example, if you plug in values in the squares where the '4' and the '33' are... then all the rest of the values are determined.
solution (spoiler)
