Brain Teaser!

Here's my take.....

The ant never gets to the end of the string

Each second, the distance  that the ant covers is   t  inches

And each second, the length of the string  (in inches)  =  12  + 12 t

So.....the ratio of the distance that the ant has traveled in t seconds  to the string length at that time is just

        t

________

12 t  +  12

As  t approaches some infinite number of seconds, this ratio   converges  to

       t                   1

_______  =      ____

   12 t                  12

Therefore, the ant can never travel much more than 1/12  the string length  as t approaches infinity

CPhill, that's a very intuitive guess!

However, there's one factor you haven't taken into account. Try to see if you can find it :)

Does the string elongate in only one direction?  If so, is the ant required to crawl that direction, or can the ant turn around and go to the static end?

This thread is comedy GOLD! 😂 Anyways, I'll tell you the thing you were missing. When the string stretches, the point the ant was on moves with it. So in theory, the ant will travel a little more than an inch and will eventually overtake the string! You can even view this in Desmos for all you visual learners.......at least that's what my teacher did! 😂 But most people do actually think that way; the ratio will always stay constant; but you must think outside the box for this one!

Good job everyone!

BasicMaths

Yeah, but unfortunately, I couldn't access my teachers laptop; I should have asked him .-.