Lions and Sheep
posted by Caprico
- January 29 2011 06:22:36 AM
There is an island filled with grass and trees and plants. The only inhabitants are 100 lions and 1 sheep.
The lions are special:
1) They are infinitely logical, smart, and completely aware of their surroundings.
2) They can survive by just eating grass (and there is an infinite amount of grass on the island).
3) They prefer of course to eat sheep.
4) Their only food options are grass or sheep.
Now, here's the kicker:
5) If a lion eats a sheep he TURNS into a sheep (and could then be eaten by other lions).
6) A lion would rather eat grass all his life than be eaten by another lion (after he turned into a sheep).
Assumptions:
1) Assume that one lion is closest to the sheep and will get to it before all others. Assume that there is never an issue with who gets to the sheep first. The issue is whether the first lion will get eaten by other lions afterwards or not.
2) The sheep cannot get away from the lion if the lion decides to eat it.
3) Do not assume anything that hasn't been stated above.
So now the question:
Will that one sheep get eaten or not and why?
Hint: Use Math induction, like on the other riddles on the site.
The lions are special:
1) They are infinitely logical, smart, and completely aware of their surroundings.
2) They can survive by just eating grass (and there is an infinite amount of grass on the island).
3) They prefer of course to eat sheep.
4) Their only food options are grass or sheep.
Now, here's the kicker:
5) If a lion eats a sheep he TURNS into a sheep (and could then be eaten by other lions).
6) A lion would rather eat grass all his life than be eaten by another lion (after he turned into a sheep).
Assumptions:
1) Assume that one lion is closest to the sheep and will get to it before all others. Assume that there is never an issue with who gets to the sheep first. The issue is whether the first lion will get eaten by other lions afterwards or not.
2) The sheep cannot get away from the lion if the lion decides to eat it.
3) Do not assume anything that hasn't been stated above.
So now the question:
Will that one sheep get eaten or not and why?
Hint: Use Math induction, like on the other riddles on the site.
Reply by Sifat
- January 29 2011 10:13:14 AM
In fact, the sheep would remain untouched if there is an even number of lions on the island, and would be eaten immediately if there is an odd number of lions on the island.
Here's the reasoning:
Consider a scenario with just one lion and one sheep: The lion will eat the sheep. Why? Because after he eats it and turns into a sheep himself, there aren't any lions on the island to eat him, so he is happy.
Now look at a scenario with 2 lions and 1 sheep. Here the sheep would remain unharmed. Why? Because if any one of them eats it, and turns into a sheep himself, he knows that he awaits certain death because he will then be a sheep and the other lion will be the only lion on the island and nothing will stop him from eating the sheep.
So now we know for a fact 1 lion and 1 sheep - sheep gets eaten. 2 lions and 1 sheep - sheep doesn't get eaten.
We can now make a conclusion about 3 lions and 1 sheep: the sheep will definitely be eaten, because the lion that eats it will know that by eating he leaves behind 2 lions and 1 sheep (himself). And as we already know 2 lions and 1 sheep is a situation where the sheep survives.
You can use the same logic to go on to 4 lions and 1 sheep, and then all the way to 100 or 1000, but it will always be true that with an odd number of lions the sheep gets eaten and with an even number the sheep doesn't.
I don't remember now but i read about the riddle somewhere i guess, to be very frank.
Here's the reasoning:
Consider a scenario with just one lion and one sheep: The lion will eat the sheep. Why? Because after he eats it and turns into a sheep himself, there aren't any lions on the island to eat him, so he is happy.
Now look at a scenario with 2 lions and 1 sheep. Here the sheep would remain unharmed. Why? Because if any one of them eats it, and turns into a sheep himself, he knows that he awaits certain death because he will then be a sheep and the other lion will be the only lion on the island and nothing will stop him from eating the sheep.
So now we know for a fact 1 lion and 1 sheep - sheep gets eaten. 2 lions and 1 sheep - sheep doesn't get eaten.
We can now make a conclusion about 3 lions and 1 sheep: the sheep will definitely be eaten, because the lion that eats it will know that by eating he leaves behind 2 lions and 1 sheep (himself). And as we already know 2 lions and 1 sheep is a situation where the sheep survives.
You can use the same logic to go on to 4 lions and 1 sheep, and then all the way to 100 or 1000, but it will always be true that with an odd number of lions the sheep gets eaten and with an even number the sheep doesn't.
I don't remember now but i read about the riddle somewhere i guess, to be very frank.
Reply by Sifat
- January 29 2011 10:13:51 AM
The sheep would remain untouched.
Forgot to give my exact answer. :P
Forgot to give my exact answer. :P
Reply by Caprico
- January 30 2011 09:55:31 PM
Ya... btw, I know you have simply copied and pasted the answers from the net. I'm leaving this site now. I had come here for some new riddles and challenges, but it turns out you were simply copying the riddles from another site, and then acting smart. You simply haven't understood the spirit or meaning of this site. Sorry man, no fun anymore...
And I was genuinely attempting all your riddles, without trying to find the riddle on the net. I just happened to come across these, and then I saw yours. Really no fun anymore, I'd rather read these riddles on the actual site, than you posting them here, and me solving them.
And I was genuinely attempting all your riddles, without trying to find the riddle on the net. I just happened to come across these, and then I saw yours. Really no fun anymore, I'd rather read these riddles on the actual site, than you posting them here, and me solving them.
Reply by Sifat
- February 01 2011 03:37:37 AM
Ok as u wish. But u,yourself were copying and pasting these riddles from another site. Isn't it the truth? And if u don't want to answer then fine. U may go and read riddles from anywhere else.
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