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A dragon and a knight live on an island where the only sources of fresh water are a pond (containing ordinary water) and six wells, numbered 1 to 6. Each well's water is completely indistinguishable from the pond water, but contains a magical poison that has no immediate symptoms, yet suddenly kills the drinker about an hour after drinking.

To make things complicated still, each well contains a different variety of poison. If a drinker who has been poisoned by a well drinks the water from another well, the result depends on the relative numbers. If the second well has a higher number then both poisons will eliminate each other and the drinker will be cured. If the second well has the same number or a lower one, it is as though the drinker had only drunk from the first well. For example, if you drink from well 1 and then from well 4 you will not be poisoned, but if you drink from well 4 and then well 1 you will be poisoned as though you had drunk only from well 4.

As a result of these rules, water from well 6 can cure poison from any of the other wells, but, when drunk by someone who is not poisoned, is incurably lethal. Furthermore, while wells 1-5 are a short walking distance from each other, well 6 is located at the top of an unclimbable mountain on the island that the knight cannot reach but the dragon can fly onto very quickly.

This sets the stage for the following puzzle: both knight and dragon understand these rules completely, know the numbering of each of the wells, and each want the other dead. Being evenly matched in combat, they arrange a special sort of duel. Each secretly fills a glass of water from one of the island's sources, then meets the other in a field, where they exchange glasses, and drink. They may seek water from any of the island's sources that they can personally reach before and after.

Is it possible for either the knight or the dragon to ensure it will survive this duel?

Note: drinking the same poison twice in a row (or 20 times in a row) has exactly the same effect as drinking the poison once.

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    $\begingroup$ Are they allowed to drink before the duel? $\endgroup$
    – oerkelens
    Nov 27, 2014 at 9:47
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    $\begingroup$ @oerkelens Yes. $\endgroup$
    – Neil
    Nov 27, 2014 at 9:48
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    $\begingroup$ If someone drinks from wells 3 then 1 then 5, does the water from well 5 cancel out with both of the previous ones, or are they still poisoned? $\endgroup$
    – Peter Taylor
    Nov 27, 2014 at 9:59
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    $\begingroup$ @PeterTaylor After drinking from well 3 then well 1, well 1 will have no effect, and so you will remain poisoned. Drinking then from well 5 well cancel out the effect of well 3. $\endgroup$
    – Neil
    Nov 27, 2014 at 10:06
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    $\begingroup$ @JamesRyan You drink from 1 and then 2. 2 counters 1, so you're not poisoned. You then drink from 3. You're poisoned again, congrats. $\endgroup$
    – Neil
    Nov 27, 2014 at 12:35

5 Answers 5

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The knight can ensure survival

by drinking from well 4 first, and 3 + 5 after. If the dragon uses pond water, or 1, 2, 3 or 4, the last drink from 5 will neutralize the others (4, ? and 3). If the dragon gives 5 or 6, it will neutralize the first '4', then 3 will be neutralized by 5.

As AeJey said, the dragon can ensure survival by

Drinking from well 5 before, and 6 after the duel.

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    $\begingroup$ Nicely done. There is more than one way that the knight can ensure survival though. $\endgroup$
    – Neil
    Nov 27, 2014 at 10:10
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    $\begingroup$ Yes, I guess any solution that replaces 4 and 3 with x (x <= 4) and y (y <= x) will work. I'm too lazy to check for a solution of another form ;) $\endgroup$
    – EagleV_Attnam
    Nov 27, 2014 at 10:13
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    $\begingroup$ You can also just drink 1 before and 1,2 after! $\endgroup$
    – Falco
    Nov 27, 2014 at 12:03
  • $\begingroup$ By the way, it also works if the one or the other brings plain water instead of poisoned water. $\endgroup$
    – Florian F
    Nov 28, 2014 at 15:02
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The other answers provide one way for the dragon to survive. A variation would be for the dragon to drink nothing before the duel, then drink from well 1 afterwards. This ensures that the dragon is poisoned -- either the knight brought pond water, and the dragon is poisoned by well 1, or the knight brought another (stronger or equal) poison, and well 1 has no effect. Drinking from well 6 now cures the dragon, regardless of which drink poisoned him.

In general, since the knight cannot reach the strongest poison, the dragon can always guarantee his survival. He can be certain that he has poisoned himself with a weak poison, either by drinking from the strongest well his opponent can reach before the duel, or the weakest afterwards. He can then cure himself at the top well.

The knight has a more convoluted play, but she can also guarantee her survival, likewise by making sure she is poisoned with a weaker poison than the strongest she can reach.

If she poisons herself before the duel with anything but the water from well 5, then depending on what the dragon brings, she will be either cured or poisoned with a weaker poison than 5's (0 here indicates the unpoisoned pond water):

Drunk from 4 beforehand -> she is now poisoned at level 4
If given: 0-4 -> still poisoned 4
Instead given: 5-6 -> cured

Drunk from 3 beforehand -> poisoned 3
If given 0-3 -> still poisoned 3
Instead given 4-6 -> cured

Drunk from 2 -> poisoned 2
Given 0-2 -> poisoned 2
Instead 3-6 -> cured

Drunk from 1 -> poisoned 1
Given 0-1 -> poisoned 1
Given 2-6 -> cured

To remove the possibility that she is cured, she can then drink from well 1. This either repoisons here, or has no effect on her already-poisoned state. Either way, she is poisoned by a well lower than 5, and so drinking from 5 now cures her.

Although the dragon alone can reach the strongest well, by poisoning herself beforehand the knight can ensure that it always acts as an antidote if she is forced to drink it. With that guaranteed, she can also always use the second strongest as an antidote.

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Yes. The dragon can ensure it will survive.

First it must drink water from well 5. Then come for the duel. After drinking the water given by the Knight (no matter if its poison-less water from the pond or poisoned water from well 1-5), it can fly to the well 6 and drink the water.

Condition 1

If the knight give him water from pond, the dragon already has drank water from well 5 which is poisonous. So it will be cured by drinking the water from 6th well.

Condition 2

If the knight give him water from any of the well 1-4, it will still have poison in it as it already drank from well 5 and it will not be cured. SO he can cure the poison by flying to well 6 and drinking the water.

Condition 3

If the knight give him water from well 5, it is poisoned, and he will still be poisoned since "drinking the same poison twice in a row (or 20 times in a row) has exactly the same effect as drinking the poison once." He can still fly to well 6 and drink the poisoned water to get cured.

The Knight Cannot make sure he will survive. He have to take his chance. The only two possible survival chances of knight are as follows.

Option 1

Knight drinking poisoned water from a lower numbered well before the duel and the dragon giving him poisoned water from a higher numbered well (preferably from well 6).

Option 2

Knight drinking nothing before the duel, and the dragon giving him pond water, thinking that the knight may have drank any of the poisonous water (preferably from well 1) before the duel.

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  • $\begingroup$ @AeJay I believe that in addition, the knight cannot guarantee his survival - if the knight drinks nothing before the exchange, the dragon just brings water from well 6 and kills him. If he drinks weaker poison before the duel, the dragon could bring freshwater which will kill him. The key point being that the knight can never guarantee his survival because the dragon has access to both the strongest poison and the placebo, while he does not. $\endgroup$
    – Joe
    Nov 27, 2014 at 9:55
  • $\begingroup$ Yes. Will add that too in my answer. Thank you. :) $\endgroup$
    – AeJey
    Nov 27, 2014 at 9:56
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    $\begingroup$ This answer is interesting, the result of not considering that the knight can still drink water after the duel :) $\endgroup$
    – justhalf
    Nov 28, 2014 at 2:12
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The dragon can always survive by drinking from well 5 before the duel and flying to the 6th well and drinking from it after the duel. (Details are mentioned in other answers before)

The knight can ensure its survival by drinking from well 1 before the duel and drinking from well 1 again after the duel and drinking from well 2 after it.
Option 1
If dragon gave him pond water or poison from well 1, it will have no effect and the knight will still be poisoned from level 1. After it, drinking from well 1 will also do nothing but drinking from well 2 after it will cure it.
Option 2
If dragon gave him any poison from level 2 to level 6, it will cure him. He will again get poisoned after drinking from well 1 and again get cured by drinking from well 2.

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First of all the dragon can always survive by drinking from well 5 before the duel and flying to the 6th well and drinking from it after the duel. (this has been mentioned in other answers with examples so I'm not giving any more)

The knight has a few options though:

The knight can drink poisoned water from a lower numbered well before the duel. Should the dragon give him poisoned water from a higher number well, that poison will outtrade the one he drank and he will be cured. (should the dragon give him pond water however he will die).

One thing I feel like no-one has touched however is a moral aspect of the question. If you had 1 hour after the duel and you didn't know what your opponent gave you you simply have to wait. Since all of the water looks exactly the same there is no telling whether or not your opponent gave you a deadly poison or harmless pond water. This is no problem for the dragon since he can drink poison from well 5 before the duel and he can ensure survival by drinking from 6 knowing that it will cancel out any poison. The knight doesn't have access to well 6 so the highest he can drink is from is 5.

Like I stated before, the knight has a moral aspect to battle. Should he decide to drink poison 1 before the duel and he believes the dragon gives him another poison (higher then 1) he wont drink for an hour (which makes a man second guess himself a lot). Does he drink poison 1 before the duel and he believes the dragon gave him pond water he drinks another poison after the fight. (this would mean suicide if the dragon actually gave him a poison).

One answer that I didn't read in the other answers is this: If the knight doesn't drink before the duel. The dragon gives him a poison. Should this poison not kill the knight instantly he knows this is not poison 6. This leaves 6 other possible drinks (poison 1 - 5 and the pond water). The knight now needs to make a moral decision whether or not the dragon gave him pond water or one of the poisons. Only poison 5 and the pond water would mean death for the knight should he decide to drink poison 5. If he decides to not drink after the duel all of the poisons would kill the knight.

There is no doubt the dragon has the upper hand in this duel, the 'safest' bet the knight can make is to drink poison 1 and hope the dragon gives him another poison higher than the one he drank.

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