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Ants On a Ruler

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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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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.

One minute.

The ants are indistinguishable.

So the same answer obtains if they pass through each other.

An ant may have to traverse the entire meter before falling off.

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Posted (edited) · Report post

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.

One minute.

The ants are indistinguishable.

So the same answer obtains if they pass through each other.

An ant may have to traverse the entire meter before falling off.

Edited by Anza Power
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Posted · Report post

when dropping ants at the same time..they can fall/land on ends

of "string thin" meter stick with other at 1000 mm /199 interval.

Should the direction probability affect the time they all fall at the

ends of the ruler? Nice programmable puzzle. Welcome sergyegi!

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less than 30 seconds if left half of ants landed facing left end of ruler while the all the other facing the other end.

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