Every second, a gun shoots a bullet in the same direction at a random constant speed between 0 and 1.
The speeds of the bullets are independent uniform random variables. Each bullet keeps the exact same speed and when two bullets collide, they are both annihilated.
After shooting 20 bullets, what is the probability that eventually all the bullets will be annihilated?
Copied from https://research.ibm.com/haifa/ponderthis/challenges/May2014.html - you might want to consult the 'solution' there before posting.
Edit: The answer in What is the probability that all the bullets will be destroyed? is not correct.
Quote from https://research.ibm.com/haifa/ponderthis/solutions/May2014.html:
Note, for example, that the same order of bullet speeds can yield different collision results: For example, let's look at two cases of four bullet speeds: A. 0.5, 0.65, 0.9, 0.6 B. 0.5, 0.8, 0.9, 0.6 In both cases, the permutation order is the same. The first bullet is the slowest, the second is the second fastest, the third is the fastest, and the last is the second-slowest. But if we examine the collisions pattern we see that A. 0.5, 0.65, 0.9, 0.6 will yield zero bullets (first the 0.9 will run into the 0.65 and then the 0.6 will collide with the first 0.5 bullet); and B. 0.5, 0.8, 0.9, 0.6 will give two live bullets forever (first the 0.8 will annihilate the 0.5, then the remaining 0.9 and 0.6 will run forever).
