bushindo

Edit: I'll just note that the intent of the puzzle is that all prisoners have to sample the wine at the same time. Since the deadline is 24 hours and the poison will take effect randomly between 12 and 24 hours after consumption, it is not possible to wait and see the effects of one wave of wine drinking before applying another.

That's a good start. It is possible to require a few prisoners less than that though. If selected as a taster, the accomplice will definitely commit suicide by drinking his own supply of poison. However, keep in mind that the emperor has many prisoners, and in the random selection procedure it is very possible that the accomplice is not chosen as a taster.

This is a variant of ujjagrawal's excellent puzzle Suppose that like ujjagrawal's puzzle, an assassin infiltrates a king's cellar and poisons 1 of the king's 500 wine bottles. Upon being detected and cornered, the assassin takes a suicide pill and dies. Anyone who consumes even the most minute amount of the poisoned wine will die between 12 and 24 hours. Consumers of the poisoned wine exhibit no other symptom besides death, and the poison can not be detected by any other means. The emperor decides to use some prisoners to taste the wine in order to determine the poisoned bottle. There is one catch, however. It is known that the assassin has precisely one accomplice among the prisoners. The accomplice has access to the same poison that the deceased assassin used to envenom one of the king's bottle. If the accomplice is chosen as one of the tasters, he will surreptitiously consume the poison regardless of which bottle he is given to drink in the hope of corrupting the deduction process. The emperor does not know which of his prisoners is the assassin's accomplice. The emperor is intrigued by this logical puzzle, and he figures that he can simply use some extra prisoners to compensate for this unknown unreliable taster. What is the minimum number of prisoners (and the tasting procedure) that he would need to use in order to correctly find the poisoned bottle among the 500 bottles within 24 hours?

Here's a play,

You're right, there is an extra layer of conditionals. We need to incorporate the information about what was said ("One of the kids is a girl") into the calculations as well.

Regarding these answers

Some comments

Thought I had a question, but it turned out to be unnecessary. Agree with Yoruichi-San on the answer. Nice puzzle!

Thought I had a nice question based on Fermat's last theorem, but turned out I was mistaken. Nice solutions, bonanova, Eventhorizon, and jim.

Here's one approach

Nice work! I think you have the correct answer. That was an attempt to think outside the box. It definitely doesn't fit the constraint of the OP unless we considerably relax the definition of 'logically deduce'

Oops, upon second thoughts, I'll revise the claim I made here

I understand your frustration of receiving no feedback after a well-reasoned and meticulous post of the solution. It is obvious from your post that you are quite smart, and I think you would fit right in this community. Personally, I generally find puzzles here to be excellent (this topic is an perfect example), and the community here includes some very fastidious, clever, and brilliant logicians. I have found myself more than once awed and humbled by the creativity and the sheer elegance of some puzzles and solutions that the Denizens come up with. I hope you will give Brainden some more time to change your opinion of its worth. I'll have to admit that sometimes it is hard to get some feedback on this board. In this case, however, you could probably initiate some discussions about the correctness of the solution by examining other solutions (bonanova's in for instance) to see whether it is incorrect or whether you missed anything. I have examined both of your solutions, and I believe both have some errors. I may be wrong, and I often am, but I'll include those possible errors here bonanova's solution voider's solution (the spoiler tags are added by me) Having said that, I'll contribute a solution of my own. This solution will give a winning chance of 42/70 or 60%.

Here's an approximative strategy,

My take on this

I'd like some clarification for the part in bold. My understanding of the trial is the following Each trial consists of the player specifying a binary sequence of length 26 (each element is either Red or Black). The host then tells the player how many elements of the sequence are correct. The player then repeats the trials, with the goal of minimizing the number of trials required in order to arrive at the correct sequence. Is this correct?

Here's a play

Here's one that gives an expected value of 3

This is a superb puzzle, plaingazed. My attempts at a solution were frustrated early due to some tunnel vision, but I did gain a lot from watching the evolution of the solution. I am in particular humbled and inspired by the plasmid's creativity and ingenuity. Thank you both for this educational experience.

I'd some some clarification. In the bold part, does it mean that the second logician predicts a card, the card is revealed, and then the logician makes the next guess, and so on?

That alternative solution is a lot more compact and elegant. Thanks for sharing this problem.

The first solution was really just a clumsy variant of the canonical solution. After that first solution I thought this is a pretty neat puzzle, but it turns out the puzzle is even more elegant than I thought. Thanks a lot for sharing this gem.

I just want to come back and say that this is a really well designed puzzle. I didn't explain the rationale behind the solution before, and so here it is

Here's an attempt.

When you say 'numbers less than 100', do you mean 'integers less than 100 but larger than 0'? Also, can a number be repeated?