As an introduction consider this one dimensional problem:
You have a number of birds sitting on a wire. At a given instant, each birds turns and looks at the bird sitting closest to it. It's pretty easy to show that 25% of the birds will not be looked at by another bird.
So lets extend this type of problem into 2 dimensions:
You have a number of hunters standing in an infinitely large field. At a given instant, each hunter turns and shoots the hunter standing closest to him (many will obviously be shot more than once). What percentage of the hunters will not be shot at all? Assume the number of hunters is large enough that any boundary conditions can be ignored.
I believe the answer to this problem is 1/e or about 37%. Does anybody solve this and come up with something different?
You have a number of birds sitting on a wire. At a given instant, each birds turns and looks at the bird sitting closest to it. It's pretty easy to show that 25% of the birds will not be looked at by another bird.
So lets extend this type of problem into 2 dimensions:
You have a number of hunters standing in an infinitely large field. At a given instant, each hunter turns and shoots the hunter standing closest to him (many will obviously be shot more than once). What percentage of the hunters will not be shot at all? Assume the number of hunters is large enough that any boundary conditions can be ignored.
I believe the answer to this problem is 1/e or about 37%. Does anybody solve this and come up with something different?