plasmid

Right you are. Sorry for the omission from the OP; this is asking for an optimal strategy, not a 100% successful strategy (which I don't think exists). The uninitiated would likely say "The more people who answer, the lower the probability that everyone will be right, so you should just designate one person to answer. Since everyone could be wearing a black or white hat regardless of what the others are wearing, the person who answers might as well answer randomly." It all seems perfectly logical on the face of it, but leads to a strategy with a 50% chance of winning instead of the 75% chance of winning that could be had otherwise. (In fact, spotting the fallacy in that logic is part of why I liked this one so much.) Now I remember bushindo posting a much more complex variation on this theme, but have yet to re-discover the original post of this puzzle.

I'm fairly sure I've seen this puzzle or something similar here before. In fact, I was trying to search for it to list it as one of my favorites in the "Best Brain Teasers" topic because if its sheer simplicity but unintuitive answer, and being the simplest case of what turns out to be an entire class of problems that can get quite complex. But my search turned up no hits If anyone's able to find the original post of this problem then please give a link so I can credit it as a favorite brain teaser. Otherwise, have a go at solving it. You and two buddies are about to play a game where the host randomly places either a white or black hat on everyone's head. You can each see the hats of the other two players, but not your own. You each get a slip of paper and may write down your guess for your hat color, which must be either "white", "black", or "abstain". If at least one person guesses their color correctly and everyone who does not abstain answers correctly, the entire team wins. If anyone guesses incorrectly or if everyone abstains, the team loses. Peeking at what the other people are writing, or any other form of communication, is cheating that will be punished by forcing the entire team to watch an episode of Sarah Palin's Alaska. What's your team's strategy?

Edit: getting used to the new editor

But I get the feeling I'm still pretty far off

Usually I only rhyme my answers if I really think I've got it. Not so in this case; only mediocre probability that this is the answer, I just rhymed because I felt like it

So that's the joyous refrain that the little schoolyard assailants in your area belt out as they're raising and lowering the lash on another, is it? Wilson wins the war of attrition against the mystery of this riddle.

This is a very good answer, even if not the one I had in mind. The first stanza's bit about being painful if held by a single flipper would certainly be true, even if it would be a very unusual move for anyone to try to make. And while the choice of the word "evade" in the third stanza seems like a strange way of describing "not losing", I can see how you could interpret it as "not letting it come all the way down towards me". At some point when it's not late I'll have to try to approach this with fresh eyes and try to gauge whether it and the thing I have in mind are comparably well fitting. But for now it's very late and tomorrow will be an early day, so I'll have to duck out simply saying that the others aren't what I'm riddling about.

Neither a mouse nor a boomerang, as there are some clues in the third verse that they don't seem to adequately explain. Winning through attrition is one such clue. The fact that "I" will sometimes act in pairs if one isn't enough is also a characteristic that might seem like it could apply to all sorts of different things, but will clearly make sense as particularly fitting for the subject of the riddle once it's revealed. At least more so than a mouse or boomerang, which aren't particularly known for acting in pairs.

I'm not sure whether or not eagles characteristically avoid flying in straight lines. More typical for that sort of behavior would be the circling of a buzzard. And turning on one's antigravity devices might be an appropriate response to an eagle attack under some circumstances, but would not be so natural of a response that it should be a clue in a riddle about an eagle. (Of course any response to a buzzard attack would be moot because the prey is typically already dead.)

Not an F-117. Since it's a single seat figher, the first stanza talking about the differences between having two people control it versus just one wouldn't seem to have a great explanation. (Not that I would recommend googling for two seater fighters as it would be a waste of time if done simply for the purpose of this riddle.) And also not a rocket. Not because it's contradicted by the body of the riddle, but because of my riddling structure. My riddles are always titled "I'm not a [decoy answer]", and although they're written to seem at first blush like they're describing the decoy answer, they're actually describing something that is most definitely very different. And I would not consider a rocket to be sufficiently different from a mortar shell to make for a good riddle.

I believe that there's quite a lot to be gained on the riddler's part if he/she reads over the answers and actually pours a bit of thought into considering whether or not they could actually fit all the clues. There are various opinions on what makes a riddle "good" (it's certainly not just the number of guesses required to get it right) and I personally think one important measure is its Eureka factor -- when it's not obvious at the outset but becomes plain as day once you see the answer that that just has to be it. Writing riddles that have that is Hard. But, if any riddler cares to hone their skills, one good way to do it is to read over the answers offered in the forum. It gives you a chance to see what sort of riddles and clues are "mushy" with all sorts of possible answers that could sort of work without being ruled out by any of the clues provided, as opposed to clues that really narrow things down. And it gives you a feel for how many such clues you'll need before the riddle is ready to fly. So, yes, the riddlers would benefit from considering the answers given and whether they might be acceptable alternate answers; not just saying "nope, not it, keep guessing" without a second thought. And while they're at it, they can credit people who come up with good answers that they hadn't considered when writing the riddle. But in my opinion, they don't necessarily need to end the riddle if they see a good alternate answer, especially if they think that the one that they originally had in mind is overall a better fit. (Believe me, when a riddle flounders for a bit and seems in hindsight to have been written too vaguely, there's actually a temptation to just say that the next answer is right and move on.) And if any riddlers don't abide by that rule, then you should demand a full refund!

Assailants in duos ensnare me with pleasure And belt out their joyous refrain If held by just one, it's so drastic a measure On self's then inflicted the pain I keep not to lines when I'm sent into action In circles and arcs are my dives Behold my approach? Then with lightning reaction Ignite antigravity drives Evade me perhaps, but I'll win through attrition Unless you're unusually skilled Then two of my kind might set out on a mission So then you're more easily killed My power... no longer suffices? Replaced by these novel devices My numbers have waned As they took the rein For sure at some much higher prices

plainglazed gets this toughie That’s why I suspected that the potential variability of the numbers could make this one a real bear. Looks like I can't add a "solved" poll because it's been over a month since it was started :·(

I never cease to be amazed by answers like chess pieces that work rather well despite not being very similar to what I had in mind. I suspect that the difficulty with this riddle has a lot to due with the fact that the numbers of these things can be variable and need not precisely match the numbers given in the riddle. To add a bit more riddling about this thing... Two for the Elven kings nearest the sky Four for the Dwarf lords who work on the stone Eight for Mortal Men puffed up with pride One for the Dark Lord in his dark home In the Land of Mordor where the Shadows lie One to reclaim the throne, no one will find them You are to bring him, and in the light bind him From the Land of Mordor where the Shadows lie A latch that locks without a key So what's inside they will not see A dozen assassins on a white plain First they stab Then they grab Then from motion restrain

edit: put everything in a spoiler, although I'm not exactly sure why given the nature of this riddle

Figures; once I finally get some time to write a riddle again, I end up without internet access for a week. shakingdavid takes this one with the little six-toed, nearly wooden-leged, "leafy" critter who would be suicidal to *not* eventually unroot itself.

You're clearly thinking along the right lines in arriving at that answer. I would accept the chandelier as an offspring of the torch or candelabra to satisfy the first stanza. But for the second, having six roots with countless leaves gets problematic. I can imagine a chandelier with six main arms and numerous smaller candle holders or lights from each of them, but even with a google image search I'm having trouble finding an example of such a construction -- if it is done, then it seems to be so uncommon that I wouldn't want to use it in a riddle.

whoops, that's supposed to be palette, not palate

Back at last, I had nearly forgotten that this one was still out there. I should probably add a bit more to give this some direction... while sticking to Tolkien. A latch that locks without a key So what's inside they will not see

Amidst the forest's my abode Not far from the branch where once I was born Where charming beauty I've bestowed On natural scenes I'm known to adorn To earth six roots branch from my greaves Encased in their bark to shield from bruise Ascending toward my countless leaves Perchance they unfurl a palate of hues Alas these roots I've come to scorn I know that without their aid I'll not stand From Mother Earth I still have torn Them up to forsake these ties to my land

After doing some Google Image searching, I have to agree with you - there can be virtually no such scattering complicating the picture in areas where there is not always significant cloud cover. However fabpig has a good point, so I also don't agree with d3k3's call of shenanigans due to the following two facts, and I revise my own answer.

While I don't normally like to nitpick just for the sake of nitpicking, there might be 7462 different possible hand ranks, but I would propose that the best way to assign a value to them would not be to give rank 7462 zero points, and rank 7461 one point, and rank 7460 two points, etc. An alternative would be to give a score to each rank proportional to its probability of winning. For rank 7462 the score would still be zero, for rank 7461 the score would be the probability that the opponent has a rank 7462 hand, and for rank N the score would be the probability that the opponent has a hand of rank less than N. (If you really want to get fancy and consider draws leading to splitting the pot evenly, then you could have the score for rank N be the sum of [proability of opponent having rank less than N] plus [1/2 x probability of opponent having rank equal to N]). If there's an easy way to calculate the number of different hands of each rank, then that might be doable. Not sure if it would change the outcome in any of the cases presented, though. Unfortunately, calculating what you would want to know for a REAL poker game -- the probability that your opponent will have a hand of a particular rank when your opponent also has the opportunity to discard (I can't imagine they would play and give only you a chance to discard) -- seems like it would be Hard.

Individual scientists when talking in private will likely say that religions are absurd, but the scientific community as a whole doesn't denounce religions such. To incontrovertibly prove my point, I'll refer to the Simpsons episode where Homer gets really smart and scientifically disproves the existence of religion and hands the proof to Ned (who promptly destroys it). It happened in parody because it hasn't yet happened in reality. While that generally has more to do with social reasons and not wanting to get your funding cut and such, the defense of "it's an untestable hypothesis so we don't have to address it" is invoked as the more purely scientific reason why the issue is ducked. The original post was a critique of that excuse. Now back to the issue of untestable hypotheses in general. One important distinction to make is the difference between something being testable and being provable. Proof is tough. Testing is much easier. With the stuff around my house, I can't prove that my microwave oven is emitting microwaves since I can't directly observe them. But I can tell that my coffee gets rewarmed if I put it in there, and infer that since it's unlikely to be getting heated by any other mechanism, then my microwave is probably actually emitting microwaves. Testable hypotheses are fine. A "working model" of the universe that's correct a lot of the time can be a handy thing. It does involve subjectivity about how much evidence something needs before you can consider it testable enough to be pretty likely to be true, but that's the situation we're stuck with. As for untestable hypotheses, like the existence of dimensions outside of the three accessible to us (plus time if you want to count it as a dimension) and wormholes and such, they have no role in anything except making for an entertaining science fiction story. It would be a completely different matter if the hypothesis would lead to testable conclusions – if gravitons were discrete particles that exerted force in quantum increments on discrete collision events as opposed to warped space-time that would have a uniform effect without such stochastic events, and if you could measure the difference between those two possibilities, then it would suddenly become a testable hypothesis that you could investigate. Or even if gravitons would, say, theoretically cause subtle influences in say the trajectories of nearby photons that warped space-time wouldn't, you could look for those influences to at least be evidence of gravitons. But unless you can come up with an experiment, the hypothesis is untestable. So, is there any role for untestable hypotheses? Like most people, my gut feeling was that they can and should be around and are nothing to be afraid of, which is part of the reason why the OP comes across as such a criticism of the assertion that religion is an untestable hypothesis and should therefore not be addressed scientifically. (The real argument behind the OP is that religion is in fact a testable hypothesis, even if not a disprovable one – just look at all the brainden posts and you'll find tons of evidence attempting to support or refute it.) But the more I think about it rationally, the more I have to admit that truly untestable hypotheses would just skew the way we think about things in ways that are probably more likely to be wrong than right. While it's true that two different untestable hypotheses might lead to vastly different outcomes, such as the Dirty Harry example, I can't come up with any rational reason to support adopting one untestable hypothesis over another if you by definition can't accumulate any evidence to support one over the other. As for the existence of multiverses, I'd say there's a fourth option for how we ended up in a universe that's so finely tuned to support life. It's that the universe doesn't really need that much fine tuning; life can arise under a lot of different conditions. While it's difficult for me to say how plausible that hypothesis is, it is perhaps a question that could be addressed by someone more knowledgeable about how many free parameters the universe has and how they would impact the ability to form complex polymers that could go on to become life as we know it. However, in the absence of such knowledge or of any discrepancies in how the observable universe would act under the two hypotheses, speculation on the existence of multiverses versus a wide range of universal parameters that could support life would fall under the category of untestable, and worth considering only until you're reasonably satisfied that they actually are untestable. (Again, I find myself compelled to entertain these untestable hypotheses, but can't rationally explain why I should!)