CaptainEd

I think I misunderstood; I guess in your description, a "turn" is the same as a "round", and the "two active players" are the two who flipped the same side of the coin. So, if they had 1,1,3 and the 3 was the odd man out, then the game is over. Have I got it this time?

If the stakes are 1,1,3, and the 3 is odd man out, which one of the 1s loses his stake to the other? I presume this is how we lose players, right?

50 sequences, avg 958.14 100 sequences, avg 959.17, max 995, min 91 it is looking like about 959. Why?<shrugs emoji>

My feeble excel simulation with n of 1000 yields 959. Sample size a meager 16 sequences. Interesting that 959 came up twice out of those 16 sequences.

If I read the picture properly, the Ogre can walk all around the lake in 8 steps. I agree that O would be foolish to tack. I was imagining a much larger lake. Sorry to disturb you guys.

This is a good clear thorough analysis of the tangential escape--a better linear escape than the straight-ahead escape or my wait-until-Ogre-has-committed-22-degrees escape. I'm sorry to be beating a dead horse, but I would now like to revisit the issue of the tacking duel. In particular, if we suppose that in the very first second of time, Ogre moves CW and Maiden moves at angle a, as determined above. Now suppose that in the next second, Ogre reverses direction ("tacks") and steps back to O's start point, moving CCW. (1) What is M's move? Does she do that recalculation you mentioned? If so, it's a different calculation, as she is now no longer directly opposite Ogre, and (in a large enough pond) hasn't gotten to a point where she has a guaranteed straightline solution. (2) If she does not recalculate, I predict the Ogre will continue moving CCW. WHEN will M do her recalculation, and what will it look like then?

You mean, when you're trying to use the editor to create a spoiler, you are unable to do so successfully? Me, too. In both Internet Explorer and Google Chrome (worse in Chrome). So what you have to do is type the explicit syntax for a spoiler. It involves a few square brackets (open and close), an equal sign, a slash, and the word "spoiler", twice. open-square-bracket the-word-spoiler equals-sign your-spoiler-title close-square-bracket all-the contents-of-the-spoiler-could be many lines open-square-bracket slash the-word-spoiler close-square-bracket. Good answer on the puzzle! I could see, among a few possibilities, that 21 is half of 42, but I had no idea how to divide by 2.

Part 2: you can have as many stones as you want. Which stones? Reference stones of my two chosen denominations? Or unknown stones?

Part 2: you can have as many stones as you want. Which stones? Reference stones of my two chosen denominations? Or as many unknown stones?

I like T-cloud's cheat. It's not a reference weight, but just a found object that represents a difference. Good outside the box thinking!

First part: do we know that all weights between 1-6 are represented in the 12 stones? Or is it possible that we have, say, 12 stones each waiting 6?

Yes, phaze, I was way off base.

Oh dear! My epsilons didn't cancel. Oops. Way to go, Bonanova!

Actually, you folks have convinced me that

OK, TSLF, thanks.

Thank you, SP and Y-san, I remember enough about calculus to know what you're saying, and even remember the notion of integration by parts. And I've heard of Mathematica. I can spell wxMaxima. I'll bet it took me more hours to do the geometry than it took you to do the calculus. (My geometry is stored in the mudroom right outside the shed) Interesting puzzle, BMAD, thanks.

Drat! You're right... Drat! You're right...I thought she could certainly spiral her way out. But a sufficiently slow-paddling maiden could actually be driven back into the center. Trickier than I thought, too.

Tricky! Edit: I agree, Bonanova, I'm not totally clear on the mechanism. A third interpretation might be that the MH reverses whenever it hits the HH. I'll take one of Y-san's Excedrins...