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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.

  Submitted by pcbouhid    
Rating: 3.1429 (7 votes)
Solution: (Hide)
The solution (found by the users) is unique. Good job! To figure out what is the correct drawing, letīs paint five cells in a chessboard pattern. There are two ways:
                    +---+            +---+
                    |   |            |///|
                +---+---+---+    +---+---+---+
                |   |///|   |    |///|   |///|
                +---+---+---+    +---+---+---+
                    |   |            |///|   
                    +---+            +---+
If (n) the number in the central cell, then the numbers (n-1) and (n+1) are in two of the others four cells. Thus, the number (n) is in a cell of different colour of the cells where are their two neighbours. In short, the even numbers and the odd numbers are in cells of different colours.

Observing the two drawings we see that the right one has 20 and 31 in cells of the same colour, so itīs the wrong drawing.

Filling the correct drawing we achieve the unique possible way (that can be found by reasoning starting near to the cells that contains 11 and 20):
               +----+----+----+----+----+----+----+
               | 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 |
               +----+----+----+----+----+----+----+

Comments: ( You must be logged in to post comments.)
  Subject Author Date
AnswerK Sengupta2009-03-06 04:22:32
re(3): Another Solution - what about...pcbouhid2005-12-01 15:42:35
re(2): Another Solution - how about...dopey9152005-12-01 14:51:19
re: Another Solution - how about...pcbouhid2005-12-01 13:54:57
SolutionAnother Solutiondopey9152005-12-01 12:18:26
re: alternate ans - nopcbouhid2005-12-01 11:09:02
alternate ansmarc2005-12-01 08:25:04
Solutioncheckmate (spoiler)Mindy Rodriguez2005-11-30 23:42:03
No SubjectMorgan2005-11-30 15:21:29
SolutionOne Solution - Spoilerdopey9152005-11-30 08:57:57
Some ThoughtsPartial SpolierSteve Herman2005-11-30 08:37:00
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