So there's this kingdom, and in the kingdom is a lake. In the lake, there's an island, and on the island is a mountain. On the mountain lives a dragon, who's been devouring all the virgins in your village.
Dismayed at this state of affairs, you beard the dragon in his lair. The dragon sneers down at you, and says "I admire your courage, little dude. Tell you what: I propose a contest of wits. On the side of the mountain, there are thirteen poisoned wells, labeled 1-13. All the poisons taste the same - just like regular water. If someone/something drinks a cup of poison from well X, they will die unless they drink another cup of poison from a well numbered greater than X (within a reasonable amount of time). For example, if I drink from well 4, I will die unless I have a cup of poison from well 5 or well 6 or well 7, etc.. So... here's what I propose. Both you and I are rational thinkers. Lets each get a cup of water (without each other seeing) and, then exchange cups. We then do whatever we think is necessary to survive, but we must drink the cup offered to us. How's that for a deal?"
Fortunately for you, you got a look at the layout of the wells on your way to the lair, and you know the dragon has an ace up his sleeve: the dragon can get his water from any of the wells; however, well 13 is impossible for you to reach, being at the very top of the mountain and surrounded by insurmountable cliffs.
Do you take the deal? If so, what is your strategy?
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9 comments:
A clarification: if you drink from well X and then from well Y > X, the second drink doesn't poison you - it is neutralized by acting as the antidote to X.
As the dragon seems to be planning to undo the effects of any low-ranking poison with his exclusive #13, one would consider giving him a cup of the conveniently available lake water, so poision 13 will kill him. But surely a rational dragon would have thought of such a scheme. And there's still the matter of surviving the dragon's cup.
I kinda agree with Steve. The dragon's gonna take his 2nd drink from well 13, no matter what you do, since he thinks it's his secret ace-in-the-hole. Fooling him with lake water will therefore kill him on the second draught. However, how can you overcome the dragon giving you well 13 water, which is what he'll do? I suppose you can do the Indiana Jones thing and just shoot 'im.
If you're confident that the dragon is going to give you Poison #13, you can inoculate yourself in advance with a cup of any of the lesser poisons. But it is a dumb dragon indeed that would expect #13 to work, when it is so obviously the secret weapon. I fear the dragon will slip you a cup #1. You'll drink yourself silly trying to both undo your prophylactic potion and also neutralize the unknown. But at least the virgins are saved.
You guys are right about how to take out the dragon. But how to save yourself? Do you have to sacrifice yourself to save the virgins? Should you decline the deal altogether?
Eric and I worked out this scheme:
Drink #1.
Drink the unknown.
Drink #1 and then #2.
If the dragon gives you lakewater, the two #1s are cured by the #2.
If the dragon gives you #1, the triple dose of #1 is cured by the #2.
If the dragon gives you #2, it cures the first #1. #1 and #2 then cancel out.
Same if the dragon gives #3 to 13.
Goodbye dragon, hello virgins!
I think we need a psychological component to this puzzle as well, though, or else the dragon will start wondering why we agreed to this competition at all. He'll realize that even if we thought we had access to well #13 when we agreed to it, the best outcome we could posssibly have hoped for is: we give the dragon #13 and he gives us #13; we both die.
Therefore we can't let the dragon start reconsidering his ace-in-the-hole. We have to give him a plausible explanation. If it once occurs to him that we could have given him lake water instead, well, he has time to torture the truth out of us before dying.
So drink stoically. And once the dragon has drunk too, heave a sigh and say, "I didn't really think you would do it. Guess we'll both die now. At least I'm not dying in vain."
And he'll say, "What are you talking about?"
And we'll say, "Well of course, we just gave each other water from well #13. There's no antidote for that."
And he'll get this incredulous look on his draconian face, and laugh in that cruel dragonish way, and say, "My boy, I [chortle] really think you need to [haha] recount those wells!"
Then, as if an awful possibility had just occurred to us, we'll go storming about the mountain, counting the wells, and finding that the last well is number TWELVE! TWELVE, OH YOU FIEND! FALSE TREACHEROUS WORM!
The dragon, pleased beyond words that his lark has resulted in such exquisite mental torment, will sigh and say, "It's not my fault that you neither have wings, nor took the time to count carefully." He'll then lift off and head for his proprietary well, secure in the knowledge that I gave him water from #12, and I'll hie back to wells #1 and #2 to save myself, before crumpling in a dejected heap to wait for the end.
Psychological considerations aside, 1-x-1-2 is the right answer.
Hmm, a little dishonorable, but then the dragon started that cycle by unilaterally devouring virgins.
There is the problem that Draco could just chomp you once you shout "Suckerrr!" and turn to leave, but he could chomp you under the "real" solution as well.
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