Edit: Now that the rules have been modified, this approach is disqualified. I'm going to leave it here in case anyone is interested until I eventually getting around to modifying it for the new rules.
Python: 277 Characters
I'm pretty sure that the generalized version of this problem is NP-Hard, and the question didn't require finding the fastest solution, so here's a brute-force method of doing it:
import itertools,string
w=[w.lower()[:-1] for w in open('w') if len(w)==6]
v=-1
for l in itertools.product(itertools.combinations(string.ascii_lowercase,10),repeat=5):
c=sum(map(lambda d:sum(map(lambda i:i[0] in i[1],zip(d,l)))==5,w))
if c>v:
v=c
print str(c)+" "+str(l)
Note that I renamed the word list file to just "w" to save a few characters.
The output is the number of words that are possible from a given configuration followed by the configuration itself:
34 (('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'))
38 (('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'k'))
42 (('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'l'))
45 (('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'n'))
50 (('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'r'))
57 (('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 's'))
60 (('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'k', 's'))
64 (('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'l', 's'))
67 (('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'n', 's'))
72 (('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'), ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'r', 's'))
...
The last line of output before the program terminates is guaranteed to be the optimal solution.
How can one count proper names considering that they vary so much across cultures? – elssar – 2013-01-21T08:20:10.123
@elssar, If I understand correctly, any word in the list is OK, regardless if it's a proper name (in any culture). – ugoren – 2013-01-21T09:28:29.780
Oh right, the in there, didn't see that – elssar – 2013-01-21T09:41:41.930
So, not a code question; but logic? – Brigand – 2013-01-21T13:05:15.533
2This is tagged as [tag:code-challenge]: what's the challenge? All you've asked for is the value which maximises a function whose domain's size is about 110.3 bits. So it's not feasible to brute-force the problem, but it should be feasible to get the exact answer, and maybe even to prove it correct. Bearing all that in mind, what are the prerequisites for an answer to be considered, and what criteria are you going to use to select a winner? – Peter Taylor – 2013-01-21T13:39:34.117
How do we handle the words with hyphens and apostrophes? – Brigand – 2013-01-21T14:08:41.550
Edited to try and clear up the questions above. – Edwin Young – 2013-01-21T15:18:48.397
+1 Lovely challenge. Anyone can produce an answer. But finding the optimal answer is far harder than it first seems. – DavidC – 2013-01-21T16:12:33.867
The current best I found was 1210 and since then just heats the room. Has anyone any higher number? @PeterTaylor: It is possible to reduce the number of bits a bit (remove combinations which for each position alone are not able to produce at least 1210 possible words). – Howard – 2013-01-21T19:06:08.383
@Howard, I looked into that when the best answer I'd seen was 1115 and it was pretty bad. My current best is 1275, and I'm about to post the code. – Peter Taylor – 2013-01-21T19:32:44.513
@Howard, in fact even with a cutoff of 1275, there are 109.7 bits of domain to brute force. Go up to a cutoff of 2000 and there are 99.5 bits, which is still impractical, and likely to exclude all actual results anyway. – Peter Taylor – 2013-01-21T19:47:58.577
Here's the word checker I'm using. Press input and replace the strings with your strings. (It'd be nice if you put this in the main question.)
– Brigand – 2013-01-21T20:37:06.197@PeterTaylor About the bits thing - just forgot the ;-) after "reduce a bit". I would be happy to see if anybody can reduce calculation time to reasonable ranges. – Howard – 2013-01-21T22:44:07.047