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.

(In reply to Not all sequences are incremental of a constant by Dej Mar)

Although ingenious, that solution doesn't fit the requirements of the problem, namely that all are arithmetic sequences. By definition an AS has a constant, i.e., fixed difference from any term to the next.

Sorry, DM!   :-)

 

Posted by JayDeeKay on 2010-02-17 14:52:00