First do a little estimation. We know we have to find four out of 16 switches, so the number of possibilities to search is only C(4,16) = 1820, so an exhaustive search will work.
These will turn on 15 lights in each set of 20, of which the number of possibilities is C(15,20)**4 = 57779667567968256L 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 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. 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. mt -- http://mail.python.org/mailman/listinfo/python-list
