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.

From 44 in the third row, the integer that begins the first row must be either 4 or 10.

If you try 4, then the number to the right of 39 must be 48. Therefore the number five places below 48 must be an even number larger than 78 (since it is 78 plus a multiple of 2) that differs from 48 by a multiple of 5. The smallest such number is 88. If you put 88 there, every other square is forced.

Edited on January 13, 2004, 5:39 pm

Posted by Penny on 2004-01-13 17:35:09