*************************************

MathMagic Cycle 11: Level 7-9 Regular 

*************************************

        I received a magazine that accidentally hadn't been stapled, and
        when I took it out of the envelope, out came pages 6 and 19 as a
        double sheet. Since some friends were laughing at my magazine, I
        told them I was able to predict not only what other pages were on
        the sheet I had in my hand, but exactly how many pages the magazine
        had. What did I have to do to in order to be correct? By working
        several different pages, can you develop a way of telling regardless
        of the number of pages?
 
**************************************

MathMagic Cycle 11: Level 7-9 Advanced 

**************************************

         ( )         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?
        \ | /
         ( )
==================
Good luck