Author Topic: The Huygens chess piece  (Read 61 times)

chilipepper

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The Huygens chess piece
« on: January 21, 2018, 11:51:27 pm »
Here's an interesting study of the huygens.
124-0
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).
125-1
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! ::)
« Last Edit: January 21, 2018, 11:56:08 pm by chilipepper »
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