bonanova

I think you've collectively touched all the bases.

Some solvers were discussing questions to which R could not respond. What door would you choose in that case? araver's approach is a solution, in that R can not respond erroneously.

OK so far. How about n=8?

araver has it. Nice solve. No lie.

I'm thinking that they do not know much if anything about each other.They all got complimentary tickets and just arrived for the show. without an evening together to plot a strategy. I'm not sure, but probably not. But hey, do any of us? . Specifically, have they already decided? Not necessarily. OK. Let's say they have not decided anything prior to hearing the question. An adequate description of the so-called "random" folk is to say that they randomly tell the truth or lie. That choice could be made [a] by coin flip, at any time prior to giving their response, and [c] with or without consultation.

araver and the Captain are so close.

Sent a note to Rookie1ja asking for help reinstating your original ID.

In solving a detective case Y-San went to her lab to use her centrifuge. It has twelve slots, spaced as the hours on a clock. She knows the importance of filling the slots in a manner that maintains proper balance, at its high operational speed. So, she wonders aloud, just loud enough for you to overhear, just how many different numbers of samples could she process at once and still maintain that balance? She of course deduced the answer as quickly as her words were formed, But she'd love to hear your thoughts on the matter as well.

You both have it. CaptainEd got it first. Congrats both.

The OP does not describe them as randomly answering yes or no.

As stated in the OP any audience member who is not a truth-teller or a liar will randomly lie or tell the truth. If you like, s/he could make that decision by coin flip.

Nice. That would get you three points of the star. But there is a more complete solution.

Variation on a familiar theme. You and two other crack Denizens participate in a competition based purely on logic. Not surprisingly, you win. But because of the large stakes involved, including but not limited to the coveted bonanova gold star, a federal investigator has been assigned to rule out any possible allegation of cheating. Think Slumdog Millionaire. Therefore You are required to explain precisely how you were able to win. Here are the facts. The host, Rookie produced eight colored stamps: four red and four blue. Two each were affixed to the foreheads of the three contestants. The remaining two were placed in Rookie's pocket. Each contestant can see the four stamps on the other two foreheads, but none can see the colors on his/her forehead, nor the two in Rookie's pocket. Rookie then asks the contestants in turn if they know their own colors. A. No, I don't. B. No, I don't. C. No, I don't. A. No, I don't. B. Yes, I do. You were contestant B. How did you convince the investigators that there was no cheating? For extra credit and the gold star, what were your colors?

Bingo.

Your analysis is right on. But clocks I've seen don't display that format (leading zero) One could say either you over-achieved, or your brightness was just unreal. Good solve.

Here's an approach I think you have it. The Ap=p is the key and A can be the first part of your matrix. Nice solve. Cap'n beat you by only a few minutes. ;(

CaptainEd, Good solve. You're on a roll.

8 1 6 3 5 7 4 9 2 Does that help?

Your clock is digital, and not of the 24-hour variety. Also it's set properly, so only valid times show. You have the right idea.

Great. You win. But what I really meant was can you draw a magic 3x3 picture?

You already know the story. Monty Hall has two doors, concealing in some order a valuable prize and a bag of garbage. But when Regis Philbin learns that the prize is $1 million, he runs onto stage and has security throw Monty out, claiming Monty has stolen his show. Regis then asks if you want to be a millionaire. Since you haven't answered any questions so far and thus have nothing to lose, you agree. He tells you that the contents behind the door of your choice are yours to keep. Which door do you choose? As an unadvertised bonus, you may use one of the standard lifelines for assistance. You reason that since none of your friends has any useful knowledge, a phone call is useless. Accordingly, you ask the computer to eliminate half of the answers. Unfortunately the computer has been programmed to eliminate precisely two answers. This is useful when there are four choices. But with only two options, it also is not useful. That leaves the audience call-out. The good news is that the audience was shown the winning door before you arrived. Every person in the audience has the information that you need to win the money. The bad news is that the audience comprises unknown numbers of truth-tellers, liars, and persons who randomly tell the truth or lie. Regis senses your sadness and offers you a choice. You may ask a single yes/no question of your choosing, either to the audience as a whole, after which you will see a tabulation of their answers, or to a single audience member, whom you may select by pointing out, from where you sit on stage. I know. This plot is worn pretty thin. But if something isn't clear, ask.. Otherwise, just tell me how much money you go home with, and how. Enjoy!

This is correct. Can you draw a picture?

Please use spoilers.