plasmid

Ok.

SMH, continuing from that last line of formula... Edit: Nevermind, I think you have to calculate the value over the range of integration for the numerator and denominator separately, I don't think you can just divide through like that. And after looking it up, those limits go to zero so I've got an indeterminate 0/0 still.

Does not compute when I try a Poisson distribution. I might be doing something wrong.

This one

Flipping the same coin twice would be indistinguishable from not flipping it at all to your buddy. So you would just be exposing yourself to more nyaning without accomplishing anything.

It looks like harey and aiemdao have sort of similar strategies, and that the number of coins flipped would be up to log base 2 of the total number of coins. With harey's answer it could be less for certain numbers of coins in play, but not for all. But if there are more than even a mere 32 coins, then you could be in for up to a solid hour of nyan-ing which might not be worth a bazillion bucks. Try for an approach with less, especially when the number of coins gets large.

I have a rare coin that’s worth a bazillion dollars and I’ll give you and a buddy a chance to win it. I’ll bring you (but not your buddy yet) into a room where I have a bunch of coins lined up in a row, probably randomly distributed between being heads up and tails up, and I’ll tell you which coin among those is the bazillion dollar coin. Then you’ll exit the room and your buddy will come in through another entrance (so you can’t communicate after I tell you which is the bazillion dollar coin) and tell me which coin to give to the two of you. That wouldn't be a very fair game, so you can also tell me to flip whichever coins you want before you leave the room and your buddy comes in. (I’m flipping them myself to make sure you don’t send codes with subtle placement of the coins or such tomfoolery.) But you have to watch 10 minutes of Nyan Cat for every coin I flip so you want to minimize the number of flips lest you go insane. I’m not saying beforehand how many coins will be in the room, and you only get one minute to tell your buddy a strategy (just words that can be spoken in under a minute, no written cheat sheets) before it’s time to play the game. Clock starts now. (I would credit the source of where I heard the original form of this puzzle that I'm modifying, but I can't remember the source any more.)

This might count as an ah-hah if it's true.

Not an answer, but a description of a potential approach and what would still be needed to make it work since this has gone for a while without being cracked.

Probably not what you have in mind, but I realized part of my previous answer was superfluous so this is a little more elegant and gets rid of some hand waving.

Right on, Cygnet! Hopefully things make sense to readers with that answer in mind, but I'll go ahead and say what I was thinking for each of the clues.

None of the above, I’m afraid. A barrel (particularly if it’s a wine barrel) could fit most of the clues except for the oddly even adulating when not dispensing slight, and for wine I would have called the roses red and white instead of pink and white while for this riddle it definitely should be pink and white. I can say that thirteen is not involved in this riddle; the oddly even among the 14 is among a natural group of 14. And a bringer of good luck is involved, but I’m looking for something that can do everything from grow the pink and white roses, adulate or dispense slight, and fit the last two lines.

I like the double meaning that would give to the clue about adulating when not dispensing slight. But alas, I can't say that was planned. Looking for something with a clearer interpretation of being "oddly even" in light of the 14 clue, and another very related thing with a clear role in invoking good luck. Maybe I shouldn't have used the word "band" in the first line; something like "gang" would work just as well without having connotations of a loop.

Two more answers to add to ThunderCloud's.

I had to read up on that one a little bit. It certainly has the blossom like a rose and could go up in flames, but not what I'm going for with this one. Still looking for something something oddly even that adulates or slights, and a weaving invoking serendipity.

The four laws of card shifting

Any stipulation for what would make one algorithm superior to another -- fewest / simplest number of commands, or fewest maximum number of moves to reach the goal? I believe I can do it with four fairly simple commands that will take a maximum of 12 moves.

Nah, no sports in particular or celebrities in general are involved in this riddle. This is something that everyone in the world will know about, although some of the clues refer to western cultural things that aren't quite completely universal.

After reading up on it a bit, at least some of the clues could be explained with that answer, but I've got to say that it would require far more specialized knowledge than I would put in a riddle meant for the general public.

Not silicon or glass, or anywhere along the elemental route. I had to do some research to see how well it would fit the clues, which obviously means it wasn’t what I had in mind. The fourteen makes sense with the atomic number, and I could see how silicon circuitry could invoke concepts of binary to explain the thing about adulating or dispensing slight. But there’s a particular reason why I chose pink and white as the colors of the “roses” that get cultivated, and I don’t think the part about serendipity when woven tight would apply to circuitry because determinism rather than luck is generally associated with electronics (at least in most people's minds to serve as a clue in a riddle).

Wow, that sure would give new meaning to the last couplet, with oxygen as the halo! Not what I have in mind, though; too many other clues would go without an explanation that I could see.

Yep, in the next-to-last sentence you give him an instruction that lets him know which of his two suspects are guilty without letting the eavesdroppers know.

Getting cooler, neither a louse nor optics.