Hi, colleagues!

A year ago coloin and me done similar work - counted e-d patterns, containing 7 clues in the first 2 bands and 27 clues in the third band (we considered not only {3,4,27} patterns, but all possible patterns beloning to this class (for example - {2,5,27} patterns)). (See thread Ask for patterns that they dont have puzzles 2.)

I found after applying 40-patterns list, that {2,5,27} patterns cannot have valid puzzles. I came to higher bound of {3,4,27} patterns which can have valid puzzles - 3428 patterns. My method was the following:

1. Write (manually) all possible maps having 7 clues in the first 2 bands and 27 clues in the third band.

2. Filter out (manually) maps by 40-patterns list.

3. Calculate (by a program) number of e-d patterns for possible maps. (This program enumerates patterns without generating them.)

If one would generate all possible e-d {3,4,27} patterns, and then apply "40-patterns list" filter, then one would get even less (than 3428) possible patterns.

Serg