Ants Go Marching: How Long Before Oblivious End?

[BobG]

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.

 

[rachmaninoff]

Hurrah! Hurrah!

 

[rachmaninoff]

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.[/color]

 

[BobG]

Wow, this got a rousing response.

Yes, the only challenge is in realizing just how simple the problem actually is.

 

[Moonbear]

Thanks, now I have that stupid children's song stuck in my head again!