The Sick Dog and the FlowerLogic puzzles require you to think. You will have to be logical in your reasoning.
Hi, my name is mister Kvakk. I live in a very big house in the country. Outside my house I have a lot of very big gardens, and it is in one of these gardens my dog (which is also my best friend) lives. But although my dog is just a dog, it has also got the ability to think. And not just that, my dog is a really smart and rational dog too.
Unfortunately, the dog is not happy. It is infected by a virus. It feels ill. The doctor says it's a 50% chance that it will die, and a 50% chance that it will be fresh again.
But in this garden where my dog lives, I have also a lot of plants. Some days ago, I put a new seed in my garden. The seed will grow up to a beautiful, red flower. So delicious will the flower be, that my dog really will want to eat it when it has grown up (yes, my dog eats flowers). But the flower is even more wonderful. If my dog eats this flower, this will kill every virus in it, and the dog will survive.
But this flower is also a very special kind of plant, because it has the ability to think too. And it is completely rational. It knows that my dog will want to eat it one day later. Therefore, the flower has the option to develop a weapon: At any time it may start to develop poison. If my dog is so unlucky to eat a flower full of poison, it will surely die, which, of course, it doesn't want to. So if the flower decides to develop poison, it's best for the dog not to eat it.
But the poison development is not an easy task to do for the flower. It doesn't want to make poison just to make poison. If it could avoid developing poison, it wouldn't do it. But, of course, the flower would like to live too, and it's better for it to develop poison than to be eaten by the dog.
Unfortunately, there is no way for the dog to see or know whether the flower has decided to develop poison or not. Both the dog and the flower know this. The dog knows, however, that the flower is just as rational as itself. The dog knows that the flower has the option to make poison, and the dog knows that the creation of poison is a hard task to do for the flower, and that it will only do it if it can save its life. In the same way, the flower knows that my dog is completely rational. My dog also knows that the flower cares only about itself. Whether the dog dies or not is irrelevant to the flower. No other red flowers will ever grow in this garden.
Let's sum up the assumptions:
1. The flower is rational and wants to make its own life as good as possible.
2. The flower knows that the dog is rational.
3. The flower doesn't want to die.
4. The flower doesn't care about what will happen to the dog.
5. The flower doesn't want to make poison. It's a hard task to do.
6. But the flower will make poison if that could prevent the dog from eating it.
7. The dog is rational.
8. The dog knows that the flower doesn't care about whether the dog dies or not.
9. The dog doesn't want to die.
10. The dog knows that the flower is rational (there is no uncertainty at this point, it knows it for sure).
11. The dog knows that the flower will make poison if that could prevent the dog from eating it.
12. The dog cannot see or know whether the flower actually makes poison or not.
13. The dog knows that the flower knows that the dog cannot see or know this.
14. If the dog eats a flower without poison it will survive. If it is poisonous it will die.
15. If the dog doesn't eat the flower, it is a 50 % chance that it will die.
So now, the question is: Will the dog eat the flower? Why or why not?
We know from assumption 5 and 6 that the flower will only develop poison if that could prevent it from being eaten. And we know that the dog knows this (assumptions 10 and 11). It therefore knows how the flower thinks, but it's impossible for the dog to actually see if the flower has produced poison or not. And the flower knows this.
Since the dog cannot see whether the flower has developed poison or not, its action must be independent of what the flower actually has done. Should the flower make poison? Remember that the dog knows for sure that the flower is rational. So, the dog should try to think what it would have done if it had been the case that it were the flower.
AnswerThe dog will eat the flower, and because the flower does not develop poison, the dog will survive. (As you can see, the flower was my medicine to the dog!)
But why will the dog eat the flower?
1. If the dog does not eat the flower, it's a 50 % chance that it will die
2. Remember further, that the dog cannot see or know whether the flower has actually produced poison or not. So what the dog decides to do is therefore independent of what the flower decides to do. If the dog has decided to eat, the flowers action cannot prevent it, and if the dog has decided not to eat, the flower cannot do any thing about this either. It has only some control over whether the dog will die or not, but it doesn't care about this.
3. The flower knows that the dog cannot know whether it has produced poison or not. Consequently, the flowers choice of action is unimportant for what the dog will do. Poison creation cannot change the action of the dog.
4. We know that the flower will only make poison if it could prevent it from being eaten. But it can't. The only reason the flower could have to make poison was to get revenge over the dog. But we know from assumption 4 that the flower doesn't want revenge.
5. That's why the flower has no reason to make poison. What the dog will do is INDEPENDENT of whether it will create poison or not.
6. The flower has no reason to make poison. Because what the dog decides to do is not dependent of whether it makes poison or not. If the dog should eat it, it will die no matter what it has done. And in that case it is best for it to not make poison, because that will make its life better. In the same way; if the dog will not eat the flower, it will be best for the flower to live a life without poison.
7. It doesn't matter what the dog will do: In any case, the flower will not produce poison
OK, this is half of the solution. We now know that the flower will not make poison. And from assumptions 7, 8, 10 and 11 we now that the dog will know this too. The dog can be fairly sure about that the flower will not make poison. This is because the dog knows that the flower is rational, and it knows how the flowers preferences are (assumptions 8 and 11). We know that the flower will not be poisonous if it is rational, and the dog will know this too. Therefore, the dog can eat the flower (and save its life!).
8. Because the dog knows that the flower is rational, it can guess how the flower might think. Therefore, it will know that the flower will not be poisonous
9. It can eat the flower. The probability of death will certainly be much higher if it doesn't.
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