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.

I agree with Steve Herman that the solution probably intends a long snake of numbers, although that is not explicitly stated, so there may be other solutions that are non-snaked.

And I also agree that the first drawing is correct, given the snake requirement.  Here is one solution:

10 11 20 21 22 23 42

 9 12 19 18 17 24 41

 8 13 14 15 16 25 40

 7 30 29 28 27 26 39

 6 31 32 33 34 35 38

 5   4   3   2  1 36 37

Posted by dopey915 on 2005-11-30 08:57:57