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MathMagic Cycle 9: Level 10-12 Regular 

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Balancing Act:
   What objects (all are the same kind) balance the last figure?

                                 O   O    X X X X       ? ? ?
    X O O       * *     * * *    X X X    O O O O 
    -----      -----    -----    -----    -------      -------
      I__________I        I________I         I____________I
           /\                 /\                   /\
          /__\               /__\                 /__\

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MathMagic Cycle 9: Level 10-12 Advanced 

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Diagonals and Triangles within Polygons:

Regular polygons have sides of equal measure. Beginning with a square,
and adding a side at a time until completing an heptagon, try to develop
relationships between the number of sides, the number of all possible
diagonals and the total number of triangles formed inside the figures.

Suggestion: Creating drawings and tables may help solve this challenge.

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Good Luck