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MathMagic Cycle 10: Level 10-12 Regular 

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         ( )         Crossed Z Hexagon:
        / | \     
     ( )--+--( )     Try placing the numbers 1 to 6 in the vertices of
      |   |  /|      of the hexagon, so that consecutive numbers (2 and
      |   | / |      3 or 5 and 6) are NOT joined by a line.
      |   |/  |
      |   *   |      How many ways of placing the numbers are there?
      |  /|   |
      | / |   |      If the vertical center line wasn't there, how many
     ( )--+--( )     arrangements would be possible?
        \ | /
         ( )

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MathMagic Cycle 10: Level 10-12 Advanced 

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        By adding and subtracting the numbers in the rows below, you can
establish relationships. Using the diagram on the left, if the relation-

   A  B  C      By adding and subtracting numbers in the rows of the
   2  6  8    figure on the left, one can establish that one of the
   1  3  4    relationships is C - A = B, so finding the values for the
   5  4  _    first and third columns should be fairly simple. 
   _  2  5                                                  
                Use the same general criteria to establish  A  B  C  D  E
              all relationships for the figure on the right 9  0  9  9  0
              and find out what numbers go in column E.     5  3  2  8  6
                                                            6  2  4  8  _
                                                            7  2  5  9  _
(Thanks to Joe Anton, Houston TX)                           2  1  1  3  2
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Good luck