bonanova

How many times a day does that happen?

How about kilometers.

A decimeter is 0.1 meter.

That's simply the AB sequence.

Switching A and B doesn't change the disparity tho, just the winner.

( i actually got this one Isn't there a better answer for part 2 tho?

Hi Generic, Yeah ... it's posted here. One way to see earlier posts is to search for example cannibals +cross. Welcome to the Den!

It might not be the answer yo are expecting but nevertheless it could be one of the answers Wow. Clapping. I think he had something else in mind from his clue, but what you found is pretty solid.

It had been a long time since Alex had dropped by Morty's. Too long, as they say. So when he happened by last night, he had some explaining to do. Well I spent a couple days looking over the puzzles the blokes there at BrainDen have been discussing. This particular one was about flipping a coin three times. There are only eight ways it will turn out, and none of them is more likely than another. Still, they didn't seem able to grasp what would happen if they raced each other one on one. Head-to-head, you might say, he added with a wink. Well it isn't all that hard to figure out, really. And so now I've got a challenge: you pick an outcome - any one you like - say three heads [HHH]. Then I'll take second choice - one of the others, say two heads followed by a tail [HHT]. Then one of us flips a coin three times. If neither pattern shows, he flips again. And again. Until the last three flips match one of the choices. Kind of like a horse race, to see which comes first. Whichever pattern shows first is the winner. Since you get first pick, you really should offer me some odds. But since I'm a nice kind of fellow, I'm offering to play you even up. Jaime looked skeptical at first, and Ian wasn't saying anything. Finally Davey spoke up. I'll play; but only if you offer me the odds: your 8 quid against my 5. Alex thought for a moment. You drive a hard bargain. But hey, it's only a game, and we're friends, aren't we? You're on! Has Davey, finally, gotten the better of Alex?

Since neither its volume nor weight changes, how do you explain a change in density?

I'll think about it ...

i had to try as you tried Good one. Now what's #2?

The last player can be said to win [normal game] or to lose [misere game]. The strategies are complementary and involve what is called the nim-sum, from the game's name. Analysis and variations can be found here and elsewhere: google nim. I didn't want to simply parrot from this link until discussion had run its course, so I only hinted in my first post. I ran into nim in college and could not master it. Hat's off to Prime for having done so.

Finally read the OP correctly. What I preach!!! A helpful term in graph theory is a clique - a monochromatically colored subgraph. In this case a group of mutual friends [duh] would be a clique, similarly a group of mutual enemies [not-so-duh].

Ouch. If the colors alternated every prisoner would say the wrong color.

Hi Lori, and welcome to the Den. A solution that has been posted a few times now, does not make any assumptions. For example.

A tesselation of 3-space perhaps?

No problem. If fact, in some puzzles it's exactly that kind of thinking that gets to the answer. That's why the wording of the OP is important. The solver has to see what's in the wording, and what is not, to arrive at valid solutions. In this particular problem, only the words red and black -nothing else, and not how the words are said - are to be used to find your own hat's color.

Agree that it's common knowledge that at least one politician exists. But the puzzle asks What, if anything, can you logically deduce from these two statements? In modern logic, the statement All P are T does not assert the existence of a P. That's why All Unicorns are Mythical Creatures makes sense, even tho there are no Unicorns [that we know of]. Or a posted sign saying All Trespassers will be Prosecuted does not imply that someone is trespassing. Also, in the example about beer, since it's common knowledge [to me anyway] that I am a man, I would not have needed that statement. Since you supplied it, I adopted a consistent approach to the puzzle question. Net: I was being picky.

TrueMaja and SCSW have it. xucam too, maybe - I'm not sure he agrees with TM or not. His edit may have gotten mangled. Multiply three different probabilities.