a problem to solve

[Michael Tobis]

Yeah,  I misread the question, but the gist of my query remains.

> The odds are 100% if there is at least one solution.

Let's not get too philosophical. My question was whether there was an a
priori reason for believing that there is a solution.

> You want permutations with replacement, so there are 8**4 = 4096

Agreed. My mistake.

>> 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

Right, but that is exactly my point. This is the number of possible
selections of 15 out of 20 made four times. Any attempt will be a
member of that space. Then the probability of hitting a solution at
random is the ratio of solutions to that space.

So I think my chance of success on a sinlge selection, assuming random
design of the switch banks, is correct: 1.9e-05 My error gave me the
wrong multiplier. It's 4096 rather than 1820. So now I'm goinq with a
7.79% chance of randomly setting up the problem to yield a solution.

Still seems somwhat unlikely that there would be a solution unless the
problem were set up in advance. (homework? a puzzle book?), I am just
wondering where the puzzle came from.

Was there more than one solution?

mt