There are 17 perfectly rational lions and 1 lamb on a magical island. Lions only eat lambs; they will not eat each other. The magical thing about this island is that if a lion eats the lamb, it becomes the lamb by magical transformation. The lions are very intelligent and live by two rules:
- Don't get eaten
- Eat a lamb only if it doesn't result in a violation of rule number 1.
To understand what happens with 17 lions and 1 lamb, one must first consider the case where there is only 1 lion and 1 lamb. The lion eats the lamb. Then consider the case of 2 lions and 1 lamb. If either lion eats the lamb, he will be a lamb in the 1 lion, 1 lamb scenario. Knowing this, neither lion will eat the lamb. Next we consider 3 lions, 1 lamb. Let's put it in a chart:
1 lion, 1 lamb: lion eats lamb
2 lions, 1 lamb: lions don't eat
3 lions, 1 lamb: lion eats lamb
4 lions, 1 lamb: lions don't eat
A pattern emerges. In situations with an even number of lions, a lamb will get eaten. In situations with an odd number, the lamb will not get eaten. Applying this rule to the case of 17 lions and 1 lamb, we see that the lamb will get eaten, leaving 16 lions and 1 lamb. At that point, the situation will remain stable.