Time for the solution to the ants on a line problem. The solution is actually stupidly simple, it really just is about one realization: Two pointlike ants bouncing off eachother is identical to two pointlike ants passing through eachother. At this point, you can easily see that there theoretical maximum is that you have an ant right on the left end initially walking to the right. No matter how the other ants are distributed, it will take exactly 100s for the last ant to fall off.
Pretty dumb puzzle, to be honest, but I thought it was a bit of a cute trick.
Showing posts with label ants. Show all posts
Showing posts with label ants. Show all posts
Ants On A Line
New puzzle time, though this one is a bit strange. I first heard it somewhere random on the blagosphere:
So, find the distribution and set of left/right choices that maximizes the time the ants spend on the stick. Or the class of distributions, I suppose, no guarantee that it is unique.
You have a one dimensional meterstick that you distribute 100 pointlike ants on, at random locations. Each ant will select randomly to begin walking right or left, and keep walking that direction at until it bumps into another ant. If two ants bump into eachother, they will each turn around and go the other direction. If an ant reaches the end of the meterstick, it will fall off. The ants have a constant speed of 1 cm/s. Given enough time, eventually all of the ants will fall off the stick, and for different initial distributions and choices of initial directions this will take a varying amount of time. What is the theoretical maximum length of time it will take for all the ants to fall of the stick?
So, find the distribution and set of left/right choices that maximizes the time the ants spend on the stick. Or the class of distributions, I suppose, no guarantee that it is unique.
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