## Tube

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Jayraj
Posts: 15
Joined: Sun Oct 21, 2018 11:06 am UTC

### Tube

In an open-ended tube, there are fifty-two round beads.

You know that one bead takes 13 seconds to travel from one end and fall off at the other.

A magnetic surge strikes the tube and each bead starts moving in a random direction.

Whenever two beads collide, they switch direction.

What is the maximum time taken for the 50th bead to fall off the tube.

ThirdParty
Posts: 347
Joined: Wed Sep 19, 2012 3:53 pm UTC
Location: USA

### Re: Tube

13 seconds, I should think. My reasoning:
Spoiler:
Think of each bead as having an arrow on it representing its direction. When beads collide, they swap arrows, but when arrows collide, all they do is swap beads and continue on their merry way. So collisions are irrelevant: each arrow takes at most 13 seconds to travel off the end of the tube.

Admittedly, the 50th vector can't have started at the very end of the tube, but we haven't been given the sort of information that would be needed to take that into account, so I assume the beads are of negligible width.

jaap
Posts: 2094
Joined: Fri Jul 06, 2007 7:06 am UTC
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### Re: Tube

This puzzle has been asked and answered here before:
Ants on a stick
Colliding balls

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