a problem to solve

[Michael Tobis]

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