Here is a simple puzzle using bullets fired at random speeds along a straight line.

Every second, a gun shoots a bullet along a straight line.

Each bullet has a random speed between 0 and 1.

Bullets do not slow down; but if two bullets collide, both of them are annihilated.

The gun stops shooting after 10 bullets have been fired.

What is the probability that eventually all the bullets will be annihilated?

Edit:

BMAD previously asked if the bullets never stop firing, whether (at least) one bullet survive forever. It inspired a lot of debate, I think without resolution. This puzzle I think has a provable answer.

For starters, solve the problem using 4 bullets.

Edited by bonanova Give credit to BMAD's earlier puzzle

## Question

## bonanova

Here is a simple puzzle using bullets fired at random speeds along a straight line.

10 bulletshave been fired.What is the probability that eventually all the bullets will be annihilated?

Edit:

BMAD previously asked if the bullets never stop firing, whether (at least) one bullet survive forever.

It inspired a lot of debate, I think without resolution.

This puzzle I think has a provable answer.

Edited by bonanovaGive credit to BMAD's earlier puzzle

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## bonanova

Here is a simple puzzle using bullets fired at random speeds along a straight line. Every second, a gun shoots a bullet along a straight line. Each bullet has a random speed between 0 and 1. Bullets

## harey

I hope I got it:

## harey

Suppose the leading bullet has 1/k chance of being the fastest. Then we will not get complete annihilation. So far, so good. But *still* we could get another collision, between other bullets. We co

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