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Forty-two pieces (Posted on 2005-11-30) Difficulty: 2 of 5
Forty-two pieces, numbered from 1 to 42, are disposed in a 6x7 grid, so that each pair of consecutive numbers are in cells that touch each other horizontally or vertically, not diagonally. Below, there are two partial drawings of the grid, where only 3 numbers appear, but only one of the two is correct.
+----+----+----+----+----+----+----+    +----+----+----+----+----+----+----+
|    | 11 | 20 |    |    |    |    |    |    | 11 | 20 |    |    |    |    |
+----+----+----+----+----+----+----+    +----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+    +----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+    +----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |    | 31 |    |    |    |    |    |
+----+----+----+----+----+----+----+    +----+----+----+----+----+----+----+
|    | 31 |    |    |    |    |    |    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+    +----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+    +----+----+----+----+----+----+----+
          (first drawing)                         (second drawing)
Justify what is the correct drawing and complete its filling.

See The Solution Submitted by pcbouhid    
Rating: 3.1429 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
No Subject | Comment 3 of 11 |
You can determine which board is correct by noticing that every odd number must be surrounded (up, down, left and right) by an even number and every even number surrounded by odds.  So, if you start with the '11' an odd, the number below must be even, and the number below that odd, then even, then odd, etc.  Therefore the second drawing cannot be correct because the 31 is in a spot that should hold an even number.  The First drawing is therfore correct.  It can be filled as follows:

10 11 20 21 22 23 42
09 12 19 18 17 24 41
08 13 14 15 16 25 40
07 30 29 28 27 26 39
06 31 32 33 34 35 38
05 04 03 02 01 36 37



  Posted by Morgan on 2005-11-30 15:21:29
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