21 replies to this topic

[swordfish]

This one is quite old, I'm posting it because I've enjoyed it immensely and want to share to those who might not have seen it yet, and to
see if anyone would present new and innovative solutions.

Here we go:

A long time ago a cruel tyrant ruled over a kingdom. One day the tyrant king heard rumors of the development of a new deadly poison in his kingdom. The rumors say that this poison comes in different potencies, the stronger ones can kill in mere minutes while the weaker ones may take some more time to take effect. Apparently the only antidote to this poison is a more potent version of itself.

Fearing that his enemies may use it against him, the king figured that he should have a vial of the most potent blend of the poison with him in case he needs it to counteract a weaker one he may ingest unwillingly. To accomplish this he called upon his two best assistants; the wizard and the witch. He gave both a week to each brew the strongest version of the poison they can; after a week they were to come back and let the king test who made the stronger poison.

The test is as follows:
The wizard and witch drinks the other's poison; then they drink their own. The person who does not die would be the one who had made the stronger poison and thus wins.

After hearing what the test was gonna be, the wizard was uneasy for he knew that the witch knows more about poisons than him and can unquestionably brew a stronger poison. With this in his mind he thought of a plan where he can guarantee his survival even if the witch's poison is superior.

The witch however is also smart, she knew the wizard knew he could never beat her and thus would resort to cheating. With this in mind the witch thought of how the wizard would cheat and thought of a counter.

A week passed and the king summoned the wizard and witch once more. They exchanged bottles and drank; they exchanged again and drank. After a few minutes, the wizard dropped dead.

Q> What was the wizard's trick? What was the witch's counter-trick?

[Prof. Templeton]

Let's see

Spoiler for knowing that

The witch makes a stronger poison, the wizard would drink his weak poison before even showing up for the test. He would then bring an nonpoisonous drink to the test. The witch would drink the nonpoisonous drink followed by her strong poison and then die. The wizard would drink the strong poison, nullifying his previous imbibement followed by his nonpoisonous drink.

The witch

Spoiler for however

knowing this fact, would also bring a nonpoisonous drink to the test causing the wizard to die from the weak poison he drank before he came.

[CaptainEd]

Spoiler for Elegant puzzle, elegant solution!

So, each person brought Water to the test, in order to kill the other! That is elegant indeed!

[bushindo]

Let's see

Spoiler for knowing that

The witch makes a stronger poison, the wizard would drink his weak poison before even showing up for the test. He would then bring an nonpoisonous drink to the test. The witch would drink the nonpoisonous drink followed by her strong poison and then die. The wizard would drink the strong poison, nullifying his previous imbibement followed by his nonpoisonous drink.

The witch

Spoiler for however

knowing this fact, would also bring a nonpoisonous drink to the test causing the wizard to die from the weak poison he drank before he came.

But it is easy to devolve into a Wine-in-Front-of-Me situation

Spoiler for

The witch, assuming that the wizard would poison himself beforehand, would bring a Water Potion to the test.

However, the wizard can easily flip the table by poisoning himself beforehand and bring a stronger Poison Potion. The witch can then counter that, and so on.

[Prof. Templeton]

But it is easy to devolve into a Wine-in-Front-of-Me situation

Spoiler for

The witch, assuming that the wizard would poison himself before hand, would bring a Water Potion to the test.

However, the wizard can easily flip the table by poisoning himself before hand and bring a stronger Poison Potion. The witch can then counter that, and so on.

Inconceivable!

[Yoruichi-san]

Spoiler for Ah, but...

Given the finite amount of time they are given to decide on a strategy, if they were game theorists, they might both alight on probabilistic strategies to determine what strength of poison they should bring and what strength of poison they should or should not ingest before hand .

Also, what does happen when you ingest three poisons in increasingly strong order? The second supposedly is the antidote to the first, so does the third re-poison the person?

[swordfish]

Let's see

Spoiler for knowing that

The witch makes a stronger poison, the wizard would drink his weak poison before even showing up for the test. He would then bring an nonpoisonous drink to the test. The witch would drink the nonpoisonous drink followed by her strong poison and then die. The wizard would drink the strong poison, nullifying his previous imbibement followed by his nonpoisonous drink.

The witch

Spoiler for however

knowing this fact, would also bring a nonpoisonous drink to the test causing the wizard to die from the weak poison he drank before he came.

This solution is correct and is in fact the simplest solution!

let's kick it up a bit then!

Spoiler for hmm

Lets say the witch didnt assume the wizard would cheat 100%, there is a chance, but there is also the possibility that he wont and would bring the strongest poison he can make or find. if the witch simply brought a non-poisonous liquid, the original solution you proposed, then they both die.
To summarize, we are now looking for a solution where the witch would survive even if the wizard cheats or not.

Spoiler for Elegant puzzle, elegant solution!

So, each person brought Water to the test, in order to kill the other! That is elegant indeed!

I thought so too

Spoiler for Ah, but...

Given the finite amount of time they are given to decide on a strategy, if they were game theorists, they might both alight on probabilistic strategies to determine what strength of poison they should bring and what strength of poison they should or should not ingest before hand .

Also, what does happen when you ingest three poisons in increasingly strong order? The second supposedly is the antidote to the first, so does the third re-poison the person?

the first two poisons will cancel eachother out leaving the third poison unchecked

P.S. The poison's effects are not invisible, I mean you dont just drop dead you feel something so you know you've been poisoned

Edited by swordfish, 18 October 2012 - 11:23 AM.

[CaptainEd]

Spoiler for If you can detect that you've been poisoned

then can we presume that there's time to apply an antidote? If so, Witch can bring Water, as before. If Wizard "cheated", by taking a weak poison before the competition and then bringing Water, Witch survives and wins If Wizard did not "cheat", but brought his best poison, Witch can detect she's being poisoned, and whip out her own most powerful brew to counteract the effects. The King may feel that's cheating and say she doesn't win. But at least she doesn't die. A further thought, if you can detect that you've been poisoned, you can also detect that you have NOT been poisoned, perhaps...But I won't go there.

[swordfish]

Spoiler for If you can detect that you've been poisoned

then can we presume that there's time to apply an antidote? If so, Witch can bring Water, as before. If Wizard "cheated", by taking a weak poison before the competition and then bringing Water, Witch survives and wins If Wizard did not "cheat", but brought his best poison, Witch can detect she's being poisoned, and whip out her own most powerful brew to counteract the effects. The King may feel that's cheating and say she doesn't win. But at least she doesn't die. A further thought, if you can detect that you've been poisoned, you can also detect that you have NOT been poisoned, perhaps...But I won't go there.

Lets say that the cruel tyrant king would be very upset when witch suddenly whips out another bottle, when it looks like she was gonna die. After all the task was to make the king the strongest poison, whats the deal with hiding a bottle of obviously stronger poison from him?

P.S. If you were afflicted with a weak variant of the poison, symptoms may take longer to manifest; it also takes longer to kill you though.

Edited by swordfish, 18 October 2012 - 05:33 PM.

[CaptainEd]

As the Witch's lawyer, I would point out that the outcome of the competition was to discover the best PERSON, not the best POISON.
Otherwise, wouldn't the Cruel Tyrant be really really upset to find that both competitors had brought Water to the competition?

In fact, this result also yields the best POISON, as the Witch may know she can do better than the Wizard, but does she have a numerical measure? Would she make her own antidote anything less than her very strongest poison? The C. T. should be glad to see what the Witch uses when she wants to save her own hide.

However, as a humble Denizen, I'm eager to solve the problem you had in mind. Does your comment imply that my solution is not a winner?

Edited by CaptainEd, 18 October 2012 - 05:39 PM.