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       #Post#: 167--------------------------------------------------
       The Huygens chess piece
       By: chilipepper Date: January 21, 2018, 10:51 pm
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       Here's an interesting study of the huygens.
       [attach=1]
       The huygens is a chess piece which jumps prime numbers of
       squares in orthogonal directions. The unusual features of the
       huygens is most evident when played on very large boards - or
       even better, on an unbounded chessboard. :)
       One of the interesting aspects of the huygens is that it is good
       at escaping attacks by other leaping chess pieces. Since a prime
       number is not a multiple of any number (except for one and
       itself), this means that every leaping chess piece must make at
       least one "non-optimal" jump when chasing after a huygens.
       The diagram below illustrates this. In the initial position, the
       black huygens on (6,0) is being attacked simultaneously by 6
       hawks and 4 knights. (A hawk jumps 2 or 3 squares in orthogonal
       and diagonal directions based on the Musketeer game definition).
       [attach=2]
       For the huygens to make an escape which frustrates these
       attackers, in can make a jump of 13 squares (one example). Every
       other piece can continue to chase the huygens, but in every
       case, the attacking piece makes at least one "sub-optimal" jump.
       This means the attacker makes a jump shorter than it's maximum
       allowed jump, or jumps in a direction which is not most-directly
       towards the huygens.
       Have fun if playing a game with the huygens - but use caution!
       Nobody knows the complete set of all prime number, so we don't
       know yet the full capability of a huygens! ::)
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