Wizard Versus the Witch

[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

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

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]

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

[bushindo]

Let's see

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

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

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

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]

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

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

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!

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.

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

I thought so too

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 October 18, 2012 by swordfish

[CaptainEd]

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]

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 October 18, 2012 by swordfish

[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 October 18, 2012 by CaptainEd

[curr3nt]

What happens then if the poisoner steals the best poison that the Witch can make to poison the Tyrant? Since the stronger poisons can kill in minutes a ready supply would have to be available and therefore subject to possible theft.

What happens when a faux potion is made to simulate the effects of the poison in order to make the target take the actual poison.

Poor, poor Tyrant is in for a nasty end regardless.

[swordfish]

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? If so, can a person detect that they're poisoned soon enough that a dose of antidote can protect them?

We have been using water to keep things simple but the witch and wizard would actually use something that looked like poison but are actually placebos (the King doesnt know what the real poison should taste like anyway) so the king would not know this unless he tests them, the placebos, himself.

What the king would see was the wizard dying and the witch surviving; suddenly the witch goes all whoozy and whips out another bottle and saves herself from dying. Right away CT knows something is amiss. He would then figure out that the two had been more concerned for their own lives than his safety; how he would act on this information is up to him.

bottom line is we are looking for a solution that keeps him in the dark.

P.S. it all depends on the strength of the poison currently active, a weak poison gives you more time to save yourself

Edited October 18, 2012 by swordfish

[swordfish]

What happens then if the poisoner steals the best poison that the Witch can make to poison the Tyrant? Since the stronger poisons can kill in minutes a ready supply would have to be available and therefore subject to possible theft.

What happens when a faux potion is made to simulate the effects of the poison in order to make the target take the actual poison.

Poor, poor Tyrant is in for a nasty end regardless.

this my friend is a riddle for another day

[Yoruichi-san]

Let's say we have poisons A, B, and C with strength A<B<C. So if someone takes A then B then C they will die, correct? What happens if they take B then A then C? Does C antidote both? Also, does the Witch know what the highest strength of poison the wizard can make is?

Witch takes a poison that is stronger than the Wizard's strongest poison but not her strongest poison before, then brings strongest poison to bout.

[Panther]

Wizard's plan - He drinks a very weak poison beforehand, then produces water (or another neutral substance) as his 'poison'. He then drinks the witch's poison, counteracting the one he took earlier, while the witch drinks his water. Then he drinks his own water, while the witch drinks her own poison, which kills her. Witch's counter-plan - She guesses the wizard's plan and makes her own 'poison' water too. They both drink water twice, but the poison that the wizard consumed beforehand kills him (assuming the wizards is not clever enough to guess that the witch will have a counter)

I'm now gonna read the other replies and probably realise that i've made some great mistake

[CaptainEd]

What if the Witch proposes a modified competition: A third (clean) goblet is to be provided by the CTK. Wizard and Witch each put some of their brew into the mixed goblet. Then each drinks the mixture, followed by their own brew. If so, Witch brings her best shot, doesn't matter what Wizard brings.

I enjoy Y-san's question about B,A,C and agree with her answer. But I doubt that the Witch has a titration measure of the Wizard's potion, so I see risk in Y's proposal.

Edited October 18, 2012 by CaptainEd

[Panther]

What if the Witch proposes a modified competition: A third (clean) goblet is to be provided by the CTK. Wizard and Witch each put some of their brew into the mixed goblet. Then each drinks the mixture, followed by their own brew. If so, Witch brings her best shot, doesn't matter what Wizard brings.

I enjoy Y-san's question about B,A,C and agree with her answer. But I doubt that the Witch has a titration measure of the Wizard's potion, so I see risk in Y's proposal.

What if the poisons simply counteracted each other in the cup?

[CaptainEd]

As the Prof said (but with more accurate phonetics), "inconshievable"!

Edited October 18, 2012 by CaptainEd

[swordfish]

whoops! 4got to check-up on this, been busy..... anyway here now!

Let's say we have poisons A, B, and C with strength A<B<C. So if someone takes A then B then C they will die, correct? What happens if they take B then A then C? Does C antidote both? Also, does the Witch know what the highest strength of poison the wizard can make is?

Witch takes a poison that is stronger than the Wizard's strongest poison but not her strongest poison before, then brings strongest poison to bout.

Theres a problem with this solution:

If wizard cheats he brings a placebo and drinks a poison weaker than the witch's(lets call this poison A).

Witch the strong poison witch drinks beforehand is poison B and witch's strongest poison is C.

Test:

exchange 1:

wiz drinks poison C = counters poison A = wizard will not die

witch drinks placebo = nothing = witch is still poisoned with poison B

exchange 2:

wiz drinks placebo = nothing = he lives

witch drinks poison C = counters poison B = witch is no longer poisoned and lives

PROBLEM: Wizard should die whether he cheats or not.

About CaptainEd's proposed modified competition; we can't/shouldn't alter the test in any way, its part of the brainteaser.

About the strength of the wizard's poison:

All i can say, because it's all I know is:

Wizard's strongest poison will always be weaker than witch's strongest poison.

Wizard's weakest poison will always be stronger than witch's weakest poison.

By how much? we don't really know exactly but the difference should be big.

Yoruichi's answer is close, it just need to go a different direction.

[phaze]

In order to make sure that the wizard does not cheat the which drinks a weaker poison than that of the wizards, but not her weakest which she presents. now if the wizard presents his weakest it will still be stronger than the one that she has already imbibed thus counter-acting it. If he presents water then he is already poisoned to a greater degree than her and her weakest potion will not change that.

The wizard however after covertly seeing the witch's preparations, poisons himself with his weakest of potions, while presenting the strongest of potions.

[Yoruichi-san]

Oh, I forgot about this, lol...

Unless the Witch can mess with the Wizard's potion, there's no way she can guarantee that both the Wizard will die AND she will not be poisoned. I was assuming she was putting her own survival first, but if she can secretly whip out a container of her strongest poison after the bout and consume it, then...

If she brings water the Wizard will die no matter whether he cheats or not, so she poisons herself with her weakest poison beforehand and brings water, and if she feels that she has not been antidoted, she secretly imbibes her strongest poison after the Wizard is dead.

Edited October 25, 2012 by Yoruichi-san

[phaze]

Oh, I forgot about this, lol...

Unless the Witch can mess with the Wizard's potion, there's no way she can guarantee that both the Wizard will die AND she will not be poisoned. I was assuming she was putting her own survival first, but if she can secretly whip out a container of her strongest poison after the bout and consume it, then...

If she brings water the Wizard will die no matter whether he cheats or not, so she poisons herself with her weakest poison beforehand and brings water, and if she feels that she has not been antidoted, she secretly imbibes her strongest poison after the Wizard is dead.

The wizard however after covertly seeing the witch's preparations, poisons himself with his weakest of potions, while presenting the strongest of potions.