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May 01, 2005

Optimal Queens

(Page 4 of 6)
May, 2005: Optimal Queens

Original                               Vertical mirror
  1  .  .  .  .                         .  .  .  .  1
  .  .  2  .  .                         .  .  2  .  .
  .  .  .  .  3                         3  .  .  .  .
  .  4  .  .  .                         .  .  .  4  .
  .  .  .  5  .                         .  5  .  .  .

90 degree rotation                   Antidiagonal mirror
  .  .  .  .  1                         .  .  3  .  .
  .  4  .  .  .                         5  .  .  .  .
  .  .  .  2  .                         .  .  .  2  .
  5  .  .  .  .                         .  4  .  .  .
  .  .  3  .  .                         .  .  .  .  1

180 degree rotation                   Horizontal mirror
  .  5  .  .  .                         .  .  .  5  .
  .  .  .  4  .                         .  4  .  .  .
  3  .  .  .  .                         .  .  .  .  3
  .  .  2  .  .                         .  .  2  .  .
  .  .  .  .  1                         1  .  .  .  .

270 degree rotation                    Diagonal mirror
  .  .  3  .  .                         1  .  .  .  .
  .  .  .  .  5                         .  .  .  4  .
  .  2  .  .  .                         .  2  .  .  .
  .  .  .  4  .                         .  .  .  .  5
  1  .  .  .  .                          .  .  3  .  .

Figure 3: Set of solutions for N=5 equivalent by symmetry operations.

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