bonanova

The flaw here is saying the first two points have a finite separation. Only then does the strip occupy 0% of the plane. You can choose any single point and call it the origin. But any other point freely chosen on the plane will be infinitely far away. Saying it another way, any other freely chosen point will have a finite separation from the first point with probability zero. Edit: This observation applies also to karthickgururaj's post #11 and following posts that discuss it.

The order of choice, by symmetry, cannot matter. The probability that A is finite is the same as the probability that B is finite. Edit: As witzar points out, the probability density function comes into play. For a probability evenly distributed over an infinite domain, that function is zero for every finite region. That is to say the probability of choosing at random any finite number from the infinite positive x-axis is zero. To see this, note that the ratio of the lengths (a) from the origin to any finite number to (b) the entire positive x-axis is zero. This is koren's argument that for an even distribution of probabilities the size of the region gives the answer. That part of his argument is not flawed. The flaw is to assign different domains for the choice of A and B. That is, to assume A is bounded while B is not. Since the premise has zero probability, so does the conclusion.

Are the tangencies all external? Are the radii all independent?

I'll still hold off with a solution for a finite circular domain. I'm very interested to see your infinite-domain solution as well.

This is a challenging puzzle. If I understand correctly, I ask someone a question then write "1" on his forehead. I might ask someone else a question then write "2" on his forehead. I then write "3" on the last person's forehead. If A raises his left hand it might mean No. If B raises his left hand it might mean Yes. Similarly for person C. After I ask my third question, I will state, for example, Number 1 is B; Number 2 is C; and Number 3 is A. Is that the idea?

Of the two questions I asked, the first is the more elegant. The answer (contact angle) is the same for any size sphere or any planet. So long as the planet's mass is large compared to that of the sphere. The second question seemed reasonable to ask, and it surprised me a little that its answer (landing point) does depend on size and on gravitational pull. On Earth, the result shows that the apple does not fall far from the tree. I also heard someone remark that the angle (in degrees) is strikingly close to the answer to life and everything. See Hitch-hiker's guide to the galaxy.

I guess I need another clarification: Is the left/right hand meaning of yes/no in some order the SAME for all the robots? It seems that it must be, but I have to ask.

Do you have any idea how long I've been trying to get a bonanova gold star? Srsly. =PEDIT: Added to profile. Another star is available for hosting Rhotus Mafia ...

I would agree that unless "some" or "all" is used as quantifier, the meaning is open to interpretation.

Slick has been offline since he posted (#3) hope he checks back.

Hi corthew, and welcome to the Den. You're right that "all" is missing from rububa's puzzle. And his use of "definitely" may have been misunderstood, as well. It's just my opinion, but I take his use of "definitely" to mean "every cog must be a pab." Or, "It is not possible that there exists a cog that is not also a pab." Since nothing in the post prohibits a non-pab cog, the question has a definite answer of FALSE. I hope you find the Den interesting, and that you will post some puzzles of your own.

plasmid's method is what actually happened in the class. It involves only counting and comparing. But honorable mention to you for tenaciously following an out of the box approach.

I'll play.

I'll take credit for turning the lynch from plas to araver. One of the more notable achievements of my brief Mafia career. araver was actually so lucid in his analysis ... and I am not ... that I took his posts for extremely skillful deception. Add to that plas's persuasion and a mad dash to make the lynch deadline. I think Goodies were done at that point.

Not quite ... a mistake solving for sin(a). Right approach.

That's an equation, in words. And symbols are algebra. The student found what might be called a constructive solution.

@Y-san. Fantastic game. Thanks for all the creative effort and narrative!

@plas, out of curiosity, who wins between you and Nana, assuming one of you is Indie?

@koren, how does your random robot answer Q1?

Knowing that and, if you're right plas surely agrees, I wonder why plas is arguing for his life tonight. There's no glory for 2nd place...

So if you had answered it would be you.

A HS Freshman class solved a problem that described a group of children with their pet dogs. They were told the number H of heads and the number F of feet belonging to the group. They were asked for the number C of children and the number D of dogs. Every student except Joe cranked out the solution using algebra. Joe nevertheless was the first one with the answer. If you eliminated the use of math, how would you solve this problem?