Starving Lions and A Goat
There are 201 starving lions in a cage with a well-fattened goat. All of the lions are really hungry and want to eat something. However, there is no point eating another starving lion, since it would take more energy to digest the food.
If a starving lion eats the well-fattened goat, he becomes a well-fed lion. If a starving lion eats a well-fed lion, then he becomes a well-fed lion.
All the lions are intelligent and understand the rules. And they know that a well-fed lion is unable to fend off a desperate starving lion.
Would the goat be eaten?
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1 solution
Suppose there are just 1 hungry lion and a goat. In this case scenario the hungry lion eats the goat as the lion has nothing to lose anyway.
Now , suppose there are 2 hungry lions and a goat. In this case scenario if one of the lions will eat the goat that lion will be eaten by the other lion and as such no lion (supposing they "play optimally") eats as they lose something. Continuing the reasoning for 3 lions and a goat , if one lion eats the goat there will be 2 lions and a well-fed lion and therefore the lion who eats the goat will not be eaten by the reasoning presented above for 2 lions and a goat. By this for 4 lions if one lion will eat the goat then there will be 3 lions a well-fed lion left (which is the same anyway therefore as the case above with 3 lions and a goat) in which it was seen that a lion will eat the goat or in this case the well fed lion , therefore because for 4 lions the lion who would eat the goat knows he will be eaten doesn't eat.
As such it can be generalized by mathematical induction that for even numbers the lions don't eat the goat beause they know they will be eaten and have something o lose while for odd numbers they know they are not going to be eaten since if they are the lion who eats them knows he will be eaten and since 201 is an odd number it anyway can be concluded that the lion will eat the goat as has nothing to lose.
It is interesting to note that if the lions will not be sure of the reasoning of the other lions maybe the lions anyway would not eat the goat at all and also it would be interesting to analyze the case for more than just 1 goat and compare for similarities with this case developing some sort of general understanding of this and rationality in considering the interaction between decision making anyway.
Therefore for broadening the understanding and considering things generally how would the case be for m lions and n goats ?
Will the lions eat the goat or will the lions not eat it ?