Ponder This — May’s Challenge!

Welcome to our “Ponder This” monthly puzzles. You are cordially invited to match wits with some of the best minds in IBM Research. Forge ahead and ponder this month’s problem!

Ponder This Challenge:

This month’s challenge is from Michael Kleber, based on a problem invented by David Wilson.

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?

Please supply the answer rounded to the 10th decimal digit.

__________

IBM Research will post the names of those who submit a correct, original solution to their website! If you don’t want your name posted then please include such a statement in your submission. Send your submission to the webmaster.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: webmster@us.ibm.com

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