# Thread: Speaking of Sheep

1. ## Speaking of Sheep

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.

But

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?

2. ## Re: Speaking of Sheep

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>The sheep is safe.
1 Lion - sheep gets eaten
2 lions - sheep safe as first lion to eat sheep would get eaten
3 lions - sheep eaten because when eaten there are 2 lions left who as shown above will not eat the new sheep
4 lions - sheep safe as if a lion ate the sheep the rule above comes into play and it know it will get eaten
5 lions - sheep eaten because yet again above rule comes into play and the lion would know it is safe
So it appears that if even number of lions the sheep is safe but odd number of lions then sheep gets eaten</font color=yellow></span hi>

3. ## Re: Speaking of Sheep

Ok, lets attack this <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow> from the other direction. Assume there is 1 lion and 1 sheep. Naturally, the lion would eat the sheep, turn in to a sheep and life happily every after.

Now, if there were 2 lions and 1 sheep - lion A would wait until lion B ate the sheep, and then eat the new sheep. Same for lion B. So, lion A watches lion B who watches lion A, etc, etc. Thus the sheep would continue in its ignorance, not knowing how close to death it really was.

So, I think that this means that we would have one stupidly happy sheet and 100 lions that watched each other like hawks.</font color=yellow></span hi>

edited by timbo - forgot to hide it

4. ## Re: Speaking of Sheep

Is this <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>right? Not that I think that it isn't - it just strikes me that there must be something wrong. Why don't 3 lions watch each other like hawks?
What happens if there were 235,423,562,352,343,452,353,244,124,521 lions? They would have to take a really quick count before they could eat (or not) the sheep.

So, basically, if we accept this, then the sheep dies the first time a new lion is born or one dies. Imagine the feeding frenzy if a lion gives birth to 3 new cubs. Cub 1 born - sheep eaten! Cub 2 born - sheep eaten!</font color=yellow></span hi>

5. ## Re: Speaking of Sheep

Have to wait for Rob's answer. <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>My first thought was the same as your reply, but when I worked out the solution based on 1,2,3... lions the pattern started to appear. There may be a dirty great big hole in my logic that I missed (won't be the first time).

The lions could always unite and have a sheep barbeque (very small portions), that way there will be 100 sheep and no lions left</font color=yellow></span hi> <img src=/S/smile.gif border=0 alt=smile width=15 height=15>

6. ## Re: Speaking of Sheep

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>I think it depends on whether or not the lions know they will turn into a sheep if they eat the sheep themselves. (Does this come under the 'they are completeley aware of their surroundings bit"?

If they don't, then the sheep will get eaten. The lion who ate it will turn into a sheep and all the other lions will learn this is not what they want to happen to them, so you will be left with 99 lions and one (newish) sheep.

If they do know, then none of them will want to eat the sheep because they in turn do not want to become sheep.
Until, that is, that a lion, realising it is about to die from old age, snaffles the poor sheep as its last supper. As it knows it was about to peg it anyway, it doesn't mind being eaten by its fellow lions.

Thus, the odds are it will get eaten.</font color=yellow></span hi>

7. ## Re: Speaking of Sheep

<img src=/S/clapping.gif border=0 alt=clapping width=19 height=23> My answer too. WRT Leif's remarks, I assumed the assumptions covered all scenarios but, Leif's Leif and thus sore a floor.

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