It doesn’t matter if #30 is correct or not. If you as prisoner ahead start with fist closed (count is odd), you cannot open fist if you hear white, nor keep it closed if you hear black. The formula for switching when you hear white doesn’t work for the #30, unless you start with a unknown state, and close it if he says white, open it if he says black. Your example said to assume ODD as start.
@DLichmann: “The formula for switching when you hear white doesn’t work for the #30, unless you start with a unknown state, and close it if he says white, open it if he says black. Your example said to assume ODD as start.”
What I think Mike was doing was saying “let’s do it like the solution presented… White from # 30 means #30 sees an odd number of white hats.”
You’re struggling with this so much that I suggest that this time you are missing the point that it doesn’t matter if #30 is right about his hat or not.
“unless you start with a unknown state” So? How do you know what #30 says before he says it?
You HAVE to assume something as a start to give an EXAMPLE.
How did the exercise with the quarters work out for you?
Piter… Right you have to assume something to start. You assume the rule, but not the state. Mike said: “I start out as if I hear white it means odd…so I close my right fists…And I keep it closed until I hear white again…” You can’t close your fist until you hear the first white.
I didn’t use your coins - but in the process of working on the problem, I laid out several examples with different numbers and orders of white and black. I was looking for a simple rule for them to follow, but didn’t find it until Mike explained it. I looked for best case and worst case scenarios… all white, all black, alternating every one. And a couple of random ones.
Thanks to both of you for the discussion!!
To MikeInNH – Throughout this discussion, I have been uncomfortable with the difficulty of mentally keeping track of the parity. Your suggestion of keeping track physically (open vs. closed fist) put my mind at ease. It has the additional advantage that if a prisoner somehow loses track, all he has to do is look at all the fists in front of him, because all the other prisoners are doing the same thing. One disadvantage, however, is that the warden may consider all of this fist opening and closing as “funny business” and take them all out to be shot.
By the way, the German keeps fish. He lives in the fourth house, which is green. He drinks coffee and smokes Prince.
alfels…Very good…You get an A.
I actually find those things fun to solve…Same with Suduku…Don’t have to have any special knowledge…just the ability to reason. When I started doing Suduku I thought it would be fun to write a program to solve a Suduku puzzle. Took me about a week to write the program…But I found it was more fun to just solve the puzzle. Some of the real hard ones would take a good half hour to solve.