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.
Earlier I gave the solution with the assumption that all of the numbers "snake". As others have stated, the checkerboard analogy is correct (odd and evens), and proves that the first drawing is the correct one...assuming the numbers "snake."
Belowis a solution where the numbers do not "snake", but as stated in the problem, each pair of consecutive numbers are in cells that touch horizontally or diagonally. In this case, the second drawing can be correct. Note that many other solutions are possible if one does not "snake" the numbers.
01 11 20 15 16 21 22
02 12 19 18 18 23 24
05 09 10 27 28 25 26
06 31 32 29 30 33 34
03 07 13 35 36 39 40
04 08 14 37 38 41 42
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Posted by dopey915
on 2005-12-01 12:18:26 |
Another Solution
