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Gauss solution of n-queens problem

  1. Oct 10, 2012 #1
    Sorry if this is the wrong section i didn't exactly know where to put this problem
    Now the n-queens problem has an arithmetic solution by Gauss:

    Suppose n is even. For any k,
    (1) If n is not 6k+2,
    j = 2i+1, for 0 <= i < n/2
    j = 2i mod n, for n/2 <= i < n
    (2) If n is not 6k
    j = (n/2 + 2i -1) mod n, for 0 <= i < n/2
    j = (n/2 + 2i + 2) mod n, for n/2 <= i
    For odd numbers, we can attach a queen at (n-1, n-1).
    source: http://bridges.canterbury.ac.nz/features/eight.html
    i don't fully understand it and where it came from
    what is the proof?
  2. jcsd
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