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Dense Mondays
arbor8
Kwon-Tom Obsessive
Puzzles: 3166
Best Total: 14m 2s
Posted - 2012.07.16 15:44:27
Foilman confirmed recently that he has upgraded a bit the code used to
generate the puzzles.One of the minor changes have been these two Friday
Beasts.Another, Monday puzzles have had more givens.
  Counting June and July 2012, average number of givens is 53,7 (ranging
from 48 to 60 ).I chose 2 random months ( Oct 2008 and Mar 2007 ) and the
average was 48,5 (from 48 to 52).
  The number of givens was always divisible by 4. Is that a coincidence
or a must-be fact?
v_e_e_n_c_a
Kwon-Tom Obsessive
Puzzles: 930
Best Total: 38m 37s
Posted - 2012.07.16 16:37:24
Quote:
Originally Posted by arbor8

  The number of givens was always divisible by 4. Is that a coincidence
or a must-be fact?

It is caused by the symmetry of puzzles plus the fact that the size of puzzle is even. For odd sizes this is not true.
Jean
Kwon-Tom Obsessive
Puzzles: 2045
Best Total: 20m 50s
Posted - 2012.07.29 04:42:17
Actually, these even-sided puzzles will always have an even number of clues, but since they have rotational symmetry rather than reflectional, the number of clues doesn't have to be a multiple of 4.  If you remove one clue, in order to keep the rotational symmetry, you would have to remove the one on the opposite side from the centre point at the same distance.  Once you did that you wouldn't have to remove the mirror image ones, though, because not all of these puzzles have mirror symmmetry.

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