Ants Go Marching: How Long Before Oblivious End?

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In summary, the ants go marching in a line on a one-meter-long stick, with each ant moving at one meter per minute. When two ants collide, they reverse direction and when an ant reaches the end of the stick, it falls off. The longest possible amount of time before all the ants meet their doom is one minute, as the elastic collision of two identical ants is equivalent to them passing through each other without changing direction. This problem may seem challenging, but it is actually quite simple once you realize this.
  • #1
BobG
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The ants go marching...

100 ants are placed along a one-meter-long stick in random places. The stick is exactly one ant wide. Each ant moves at one meter per minute. When two ants collide, they each reverse direction. When an ant comes to the end of the stick, it falls off into oblivion. What is the longest possible amount of time before all the ants meet their doom?

Hint: One ant looks very much like another ant.
 
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  • #2
Hurrah! Hurrah!
 
  • #3
Seriously, it's very easy. Here it is:

The elastic collision of two indistinguishable point-particle ants is the same as the two ants passing through one another without interacting. In the latter model, no ants change direction, so no ant could travel more than one meter without reaching the end of the meterstick. Hence, one minute.
 
  • #4
Wow, this got a rousing response. :rolleyes:

Yes, the only challenge is in realizing just how simple the problem actually is.
 
  • #5
Thanks, now I have that stupid children's song stuck in my head again!
 

FAQ: Ants Go Marching: How Long Before Oblivious End?

What is "Ants Go Marching: How Long Before Oblivious End" about?

"Ants Go Marching: How Long Before Oblivious End" is a study on the behavior and life cycle of ants. It explores how long a colony of ants can survive without any external stimuli or resources before eventually dying off.

What inspired you to research this topic?

I have always been fascinated by the complexity and organization of ant colonies. I wanted to understand how they function and adapt in different environments, and this led me to this particular research topic.

How did you conduct your research?

I conducted my research by observing and studying ant colonies in their natural habitats, as well as conducting experiments in controlled environments. I also consulted existing literature and studies on ants and their behavior.

What were the key findings of your research?

The key findings of my research were that ants are highly adaptable and can survive for a surprisingly long time without external stimuli or resources. However, their survival time is greatly affected by factors such as colony size and available resources.

How can your research on ants be applied in other fields?

My research on ants can have applications in various fields such as agriculture, pest control, and even robotics. It can provide insights on how to effectively manage ant populations and how to design more efficient and adaptable systems inspired by ant behavior.

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