A friend emailed me this; I am absolutely clueless. Any help would be greatly appreciated:
A dragon and knight live on an island. This island has seven poisoned wells, numbered 1 to 7. If you drink from a well, you can only save yourself by drinking from a higher numbered well. Well 7 is located at the top of a high mountain, so only the dragon can reach it.
One day they decide that the island isn’t big enough for the two of them, and they have a duel. Each of them brings a glass of water to the duel, they exchange glasses, and drink. After the duel, the knight lives and the dragon dies.
The Knight drinks from well 1 before the duel. Thus when he drinks the water the dragon brings he is not poisoned but cured becasue he drinks from a higher well.
The Knight brings the dragon sea water. So when the dragon drinks from well 7, thinking to cure himself, he really poisons himself with any cure.
I am SO useless with riddles, that the mere danger of me trying to think this one through had me scurrying off, fast, fast, fast, to our beloved friend Google. All the same - in case someone is really bothering to think for an answer, I’ll just post the link to the answer, then everyone can be happy.
The dragon and knight both know that there is no cure for well 7. They presumably also know that 7 acts an antidote and not a poison, if water from a lower-numbered well is consumed prior.
The dragon could very well anticipate that the knight anticipates the dragon to bring well 7 water, hence bringing sea water or well 1 water. Thus poisoning the knoght. What makes this line of reasoning and indeed the puzzle incomplete is that time of onset of the poison’s effects are unclear. Does it act immediately? 2 hours? 2 days?
Similarly, the dragon could anticipate that the knight would anticipate the dragon’s knee-jerk visit to well 7, hence bringing regular water (since the knight is well-aware that any poisoned water he can bring will be neutralized by dragon’s trip to well 7).
The solution must account for these foresights and yet produce the end result (knight -> alive, dragon -> dead).
My solution for the second bit was to have the knight bring water from two wells (I assume the dragon can tell seawater from well water at least).
BUT! what if the dragon (being almost Sicilian in sneakery) brings water from well #1? Then the knight is poisoned twice over!
You can resolve this by having the poison work slowly enough for the knight to consume his secret supply of #2 water (um… ugh. Yaknowhatimean) if he finds himself starting to foam, whilst the dragon has likewise pre-emptively counteracted the “poison” by drinking from #7 and has no recourse.
BUT!! (again) - the smart dragon could follow the same procedure as the savvy knight with wells 6 and 7. I think you just have to pretend that none of the individuals involved are familiar with game theory, logic analysis, etc. (Or perhaps put some rules on the poison I’m not willing to work out at 5am)
That site looks interesting - I took a few logic courses to go with my C.S. degree a while back; I’ll have to break out the books again.
I think it’s implicit that the knight has time to drink from any well. OTOH, I think you can’t know if you’re poisoned (or the dragon would have to be quite stupid to drink from #7)
My resolution would be: the knight had a cache of #1 and #2. The dragon handed him #?. He drinks #1, then #? then #1 then #2. If ?=1 (or seawater), he’s poisoned by #1 thrice (twice) but cured by #2. If ?=2,3… then he’s poisoned, cured, repoisoned, recured. Either way, he ends up safe.
I’m still working on the most reasonable reason why the knight was cleverer than the dragon.
The knight drinks as per Shade’s double-formula. However, when the dragon lifts his glass to drink, the knight pulls out his sword and runs the dragon through the throat.
Anything the knight can do, the dragon can do, but the reverse is not true. This gives the dragon a dominating advantage. Nonetheless, the knight lives, and the dragon dies. Therefore, we are forced to conclude that the knight is cleverer than the dragon. Why is the knight cleverer? Depends on what you mean by “why”. If you mean “how do we know”, then we know because the knight won. If you mean “what was the underlying cause”, that’s not relevant to the riddle.
Nitpick: is your reasoning sufficient there, Chronos? What about competitions where the optimum strategy is to some extent random? Can’t then the disadvantaged player win with both being equally perfectly clever?
Chronos has it right here, we are given the outcome to the duel, and asked to explain that, we are not asked what the optimum strategies are.
There are many combinations of wells that lead to the same outcome, for instance, D gives water from W2 and K having already drank water from W1 survives, meanwhile K gives D water from W5 and D takes water from W3 to as an antidote, but this fails.
Such a scenario is unsatisfying and leaves too many questions – indeed, the challenge is to find the most satisfying scenario that leaves the minimum (preferably zero) number of questions.
Specifically, we have to adequately explain how D could lose, when D has the utmost antidote! (And also, how can K survive given that D has the ultimate poison)
K giving D sea-water is a fairly elegant solution, perhaps spoiled by the fact that presumably D would recognise the salty taste, but it could be argued that though D tastes the salt, D suspects that K has mixed salt-water with water from W6. (Another “solution” is that K gives water mixed from W1 and W2 (if we can assume from the rules that such a mix is non-toxic(?))) .
Anyhow, the fact that D plays the game imperfectly is a given in the puzzle, we are not asked to explain this deficiency.
The Great Unwashed Anyhow, the fact that D plays the game imperfectly is a given in the puzzle, we are not asked to explain this deficiency.
Then why come up with any solution more elaborate than D giving K sea-water and K giving D sea-water as well?
We are given to assume that
K and D both want to survive
K and D are both aware of the effects of well water and the intricacies of how they combine
K and D are both intelligent enough to work towards their goal of survival.
After all, all solutions proposed, implicitly factor in some anticipation on part of the two opponents. If not, why would the knight drink well 1 waer beforehand in some solutions?
IMHO, the key to solving this riddle is to come up with a solution that either factors in all anticipations, barring which, is independent of all anticipations.
Given the limited information about the poisons, their time of onset and their combinations …etc, this is a poorly defined riddle.
Then again, perhaps the problem statement should be interpreted literally:
If you drink from a well, you can only save yourself by drinking from a higher numbered well.
Thus drinking from any well means inevitable death after one eventually drinks from the highest well available.
If we assume that ‘the knight lives’ means he is no longer poisoned, then the dragon could not have brought any poisoned well water (so he brought sea- or freshwater). The knight brought water from any poisoned well he wished, which meant the dragon would die.
It’s at least as plausible as any other explanation, and leaves few questions as to what actually happened.
