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Hound Path (Posted on 2013-06-27) Difficulty: 3 of 5
+--+--+--+--+--+
|  |  |  |  |11|     
+--+--+--+--+--+
|  |  |  |  |  |     
+--+--+--+--+--+
|  |  |  |  |  |     
+--+--+--+--+--+
| 5|  |  |19|  |     
+--+--+--+--+--+
|  |  |  |  |  |     
+--+--+--+--+--+
A hound started on a square numbered 1, and moved from square to square numbering them in succession to the last one, numbered 25. The hound never entered any square twice and moved horizontally and vertically only, except for one diagonal move to a neighboring square.

All the numbers except those shown were then deleted. Figure out the path of the hound.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 1 of 2

The single diagonal allowed must come between the 5 and the 11. But it must not be allowed to cut off any path (no diagonals allowed) from 11 to 19 or 19 to 25. Since at least one cell must be cut off in the upper left, the numbers 1 - 4 must be there, hugging the wall:


+--+--+--+--+--+
| 2| 1|  |  |11|    
+--+--+--+--+--+
| 3|  |  |  |  |    
+--+--+--+--+--+
| 4|  |  |  |  |    
+--+--+--+--+--+
| 5|  |  |19|  |    
+--+--+--+--+--+
|  |  |  |  |  |    
+--+--+--+--+--+

Placing the diagonal immediately after the 5 results in an impossible situation when trying to complete the path from 19 to 25, so the 5 is connected by placing the 6 to the right of the five. Of course the numbers must hug the previously placed numbers so as not to cut off 11-19 or 19-25.

+--+--+--+--+--+
| 2| 1| 9|10|11|    
+--+--+--+--+--+
| 3| 8|  |  |  |    
+--+--+--+--+--+
| 4| 7|  |  |  |    
+--+--+--+--+--+
| 5| 6|  |19|  |    
+--+--+--+--+--+
|  |  |  |  |  |    
+--+--+--+--+--+

Trial and error leads to:

+--+--+--+--+--+
| 2| 1| 9|10|11|    
+--+--+--+--+--+
| 3| 8|16|15|12|    
+--+--+--+--+--+
| 4| 7|17|14|13|    
+--+--+--+--+--+
| 5| 6|18|19|20|    
+--+--+--+--+--+
|25|24|23|22|21|    
+--+--+--+--+--+

  Posted by Charlie on 2013-06-27 12:54:29
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