by susume » Mon Oct 27, 2008 5:19 pm
In Mauricio's last 5 puzzles above, as in #020#tarek-007, the jellyfish can be seen before any pencil marks are entered, because the spaces where PMs must go are jellyfish-shaped. There are 4 columns in which the givens occupy the same 4 rows, leaving spaces only in the other 5 rows of those columns. If a digit is not included in the 4x4 subset of givens, but does appear once in a row outside that subset, it forces the candidates for that digit into the remaining 4 rows of those 4 columns - i.e. a jellyfish. In Mauricio's last 5 puzzles, there are three such digits excluded from the 4x4 subset of givens and given once outside the subset - hence 3 jellyfish visible before any PMs. Since the same givens in these puzzles can also be viewed as 4 rows with givens in 4 columns, and the excluded digit's given eliminates a 5th column, each of the excluded digits actually produces two complementary jellyfish, for 6 jellyfish per puzzle visible before any PMs. Any time one sees givens arranged this way, it may be worth looking for jellyfish earlier than one ordinarily would.
):