Polylines and Polysticks

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Polylines can be regarded as unit lines confined to the square grid. I use the convention that polylines are allowed to cross each other, whilst polysticks cannot. Physical pieces can be constructed for the polysticks in a number of ways.

  Monostick - 1 (1 line)

       

  Disticks - 2 (4 lines)

     
1 2      

  Tristicks - 5 (15 lines)

1 2 3 4 5

  Tetrasticks - 16 (64 lines)

1 2 3 4 5
I L Y N V
6 7 8 9 10
W T Z R X
11 12 13 14 15
U F H P J
       
16        
O        
         

 

  For higher orders of polylines, the number of pieces is as follows:

  Pentasticks - 55

  Hexasticks  - 222

  Heptasticks - 950

  Octasticks   - 4265

 

Puzzles using Polysticks

 

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