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# Ants On a Ruler

Best Answer bonanova, 19 January 2013 - 07:11 AM

You have a one meter ruler. We will drop 200 ants on to the ruler, each ant falling at a location along the ruler which is uniformly distributed. When an ant falls, it goes left or right with equal probability. When two ants bump into each other they reverse directions. Each ant moves along the string at a speed of 1 meter per minute. How long will it take for all the ants to fall off the ruler?

Hi sergyegi, and welcome to the Den.

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4 replies to this topic

### #1 sergyegi

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Posted 19 January 2013 - 02:24 AM

You have a one meter ruler. We will drop 200 ants on to the ruler, each ant falling at a location along the ruler which is uniformly distributed. When an ant falls, it goes left or right with equal probability. When two ants bump into each other they reverse directions. Each ant moves along the string at a speed of 1 meter per minute. How long will it take for all the ants to fall off the ruler?

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### #2 bonanova

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Posted 19 January 2013 - 07:11 AM   Best Answer

You have a one meter ruler. We will drop 200 ants on to the ruler, each ant falling at a location along the ruler which is uniformly distributed. When an ant falls, it goes left or right with equal probability. When two ants bump into each other they reverse directions. Each ant moves along the string at a speed of 1 meter per minute. How long will it take for all the ants to fall off the ruler?

Hi sergyegi, and welcome to the Den.

Spoiler for looks like

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Vidi vici veni.

### #3 Anza Power

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Posted 19 January 2013 - 11:33 AM

You have a one meter ruler. We will drop 200 ants on to the ruler, each ant falling at a location along the ruler which is uniformly distributed. When an ant falls, it goes left or right with equal probability. When two ants bump into each other they reverse directions. Each ant moves along the string at a speed of 1 meter per minute. How long will it take for all the ants to fall off the ruler?

Hi sergyegi, and welcome to the Den.

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Edited by Anza Power, 19 January 2013 - 11:33 AM.

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### #4 TimeSpaceLightForce

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Posted 19 January 2013 - 06:39 PM

Spoiler for

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### #5 TimeSpaceLightForce

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Posted 19 January 2013 - 10:20 PM

Spoiler for shortest possible time

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