Fortytwo 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     
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          31      
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  31              
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(first drawing) (second drawing)
Justify what is the correct drawing and complete its filling.
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 20051130 15:21:29 