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.

Following is an alternate solution.  Though some of the following sequences will eventually decrease, within the scope of the "grid" they increase.

   +--+--+--+--+--+
   | 4| 6| 9|13|18|
   +--+--+--+--+--+--+--+
   |13|XXXXXXXX|30|39|48|
   +--+XXXXXXXX+--+--+--+
   |22|XXXXXXXX|44|XX|60|
   +--+XXXXX+--+--+--+--+
   |31|XXXXX|48|60|68|72|
+--+--+--+--+--+--+--+--+
|34|40|45|49|52|XXXXX|84|
+--+--+--+--+--+XXXXX+--+
|35|XXXXXXXX|57|XXXXX|96|
+--+XXXXXXXX+--+--+--+--+
|37|XXXXXXXX|63|78|93|108|
+--+--+--+--+--+--+--+--+
|40|49|57|64|70|
+--+--+--+--+--+

 4...(+2)...6...(+3)...9...(+4)...13...(+5)...18   
30...(+9)...39...(+9)...48
48...(+4*3)...60...(+4*2)...68...(+4*1)...72
34...(+6)...40...(+5)...45...(+4)...49...(+3)...52
63...(+15)...78...(+15)...93...(+15)...108
40...(+9)...49...(+8)...57...(+7)...64...(+6)...70

 4...(+9)....13...(+9)...22...(+9)...31...(+9)...40
18...(+6*2)....30....(+7*2)....44....(+8*2)....60
48...(+12)..60...(+12)..72...(+12)..84...(+12)..96...(+12)..108
34...(+1)...35...(+2)...37...(+3)...40

Posted by Dej Mar on 2006-05-06 22:23:17