Michael Tobis wrote: > First do a little estimation. We know we have to find four out of 16 > switches,
4 panels, eight switches each, 32 total. > so the number of possibilities to search is only C(4,16) = > 1820, so an exhaustive search will work. Yes, but for the wrong reason. It's not combinations, the switch selection A = 1 B = 2 C = 3 D = 4 is not the same as A = 4 B = 3 C = 2 D = 1 You want permutations with replacement, so there are 8**4 = 4096 possibilities, which is still tractable. > > These will turn on 15 lights in each set of 20, of which the number of > possibilities is C(15,20)**4 = 57779667567968256L No, there are only 8 possible patterns on each panel. Not every possible 15 lamp pattern is realized. > > The number of these that are successes is the number of ways to pick 3 > out of 4 twenty times: 4**20 = 1099511627776L > > For each pick, your chance of success is then > float(1099511627776L)/57779667567968256L = 1.9029386530869287e-05 Chance doesn't enter into it. Unless you ask what is the chance that a randomly selected switch pattern is a solution? But no one is asking that. > > You get 1820 distinct tries. Assuming no overlap (which slightly > overestimates your chances if it's a false assumption), the odds that > there is a solution are > > 1820 * 1.9029386530869287e-05 = 0.034633483486182101 > > or about 3.5%. Not great. The odds are 100% if there is at least one solution. > > There seem to be some symmetries I haven't used, which may conceivably > help your cause. I just wonder if you have some basis for beleiving > that there is a solution. There is. I solved it using the technique I outlined in my previous posts. > > mt -- http://mail.python.org/mailman/listinfo/python-list
