Hard Riddle #1

@TakeThePawnOrLose
Is this a team forum that someone didn't ask questions so you are doing the job! Also, @)gloweyysquidd used to ask riddles not math questions.
Plus this question is wrongly stated as something seems strange while solving as if you made it yourself!

Suppose you have a rubber band of circumference 1 meter. This rubber band is growing at a rate of 1m/s
Already 1m circumference and speed 1m/s. Comparative speed is much higher than in comparison with body. It might outrun Usain Bolt!

@Akbar2thegreat said in #11:

Already 1m circumference and speed 1m/s. Comparative speed is much higher than in comparison with body. It might outrun Usain Bolt!
Usain Bolt height: 1.95 m
Usain Bolt peak speed: 43.99 km/h=12.22 m/s.

Also it's kind of weird that your only issue with a rubber band that magically grows longer and longer without ever breaking, with a tiny robots moving on it without ever falling down, is that the growth speed is not realistic.

@FC-in-the-UK said in #12:

Usain Bolt height: 1.95 m
Usain Bolt peak speed: 43.99 km/h=12.22 m/s.
You don't get it!
The unbreakable rubber band of OP in question increases itself by its own size every second!
While a human runs forward but their height remains same!
It was a joke after all, but you still didn't get it!

Anyone who said that it can, you were correct. For the correct explanation, see #8 where @CalbernandHowbe more or less gave the exact explanation (I don't understand why that was disliked, is it because they dragged calculus into this?).

@Nomen-Nonatur The problem is well defined. A rubber band is a circle, and therefore, if it is growing at a rate of 1 m/s, it essentially means that the diameter is increasing as the circumference is pi*diameter (pi is a constant and therefore can not increase). If the diameter is what is increasing, then the increase in circumference will be distributed throughout the circle.

AS for why I posted a "math problem", almost everyone knows the basic riddles and it would be very boring if I asked some basic riddle. The point of a forum is to communicate with people, there is no communication if the first person to say something gets the correct answer. If no one likes these kinds of problems, then I won't post them, just let me know.

@ TakeThePawnOrLose said in #1:

Since @GloweyySquidd stopped posting riddles, I guess I will take over at least for the moment. Though you are more than welcome to take back over.

Here is the riddle: Suppose you have a rubber band of circumference 1 meter. This rubber band is growing at a rate of 1m/s and has a the quality that it can expand to maximum radius of infinity meters. On this rubber band, there is a small robot that starts off at point x. This robot is specially programmed to move only on the rubber band. If the robot moves with a velocity of 0.5 m/s from time, t = 0 to t = infinity, does the robot ever reach point x ever again?

Explain your answer with math or logic.

If the rubber band is growing at 1m/s and the dumb robot at 0.5m/s , the robot isn't fast enough to double the growing speed of the rubber band and therefore he can never reach the other side, even with an infinite time.

Graphically, it would look like this:
https://i.imgur.com/Zacwtop.png

See? Both functions are linear functions (written : f(x) = a*x ) which means they only intersect on one point: the Origin (0;0). It also means they can't intersect anywhere else on the graph. And if they can't intersect anywhere else, we've proven that the distance between the robot and the end of the rubber band, and so we conclude that that stupid robot will never make it at the end.

@WassimBerbar read #8

@WassimBerbar said in #16:

If the rubber band is growing at 1m/s and the dumb robot at 0.5m/s , the robot isn't fast enough to double the growing speed of the rubber band and therefore he can never reach the other side, even with an infinite time.

Graphically, it would look like this:

See? Both functions are linear functions (written : f(x) = a*x ) which means they only intersect on one point: the Origin (0;0). It also means they can't intersect anywhere else on the graph. And if they can't intersect anywhere else, we've proven that the distance between the robot and the end of the rubber band, and so we conclude that that stupid robot will never make it at the end.

Let me try to explain this.
Lets try and make a table for the circumference as a function of time vs the position of the robot as a function of the time.

Time, Circumference(t), Robot(t)
t = 0, 1, 0
t = 1, 2, 0.5
t = 2, 3, 1
t = 3, 4, 1.5
t = 4, 5, 2
t = 5, 6, 2.5
t = 6, 7, 3
t = 7, 8, 3.5
t = 8, 9, 4
t = 9, 10, 4.5

The amount the robot covers by t = x is position(x)/circumference(x).

So, now let's make a table for the amount covered as a function of time
Time, Amount covered(t)
t = 0, 0/1 = 0 = 0%
t = 1, 0.5/2 = 0.25 = 25%
t = 2, 1/3 = 0.333.... = 33.33....%
t = 3, 1.5/4 = 0.375 = 37.5%
t = 4, 2/5 = 0.4 = 40%
t = 5, 2.5/6 = 0.41666.... = 41.666....%
t = 6, 3/7 = 0.42857 = 42.857%
t = 7, 3.5/8 = 0.4375 = 43.75
t = 8, 4/9 = 0.444.... = 44.444...%
t = 9, 4.5/10 = 0.45 = 45%

As you can see, the percentage of the rubber band that the robot has covered increases over time. If you let this time go on, you would eventually reach 100% which means that the robot will reach point x again.

@TakeThePawnOrLose no this percentage will never reach 100%, the limit as this series goes to infinity is 50%. (n-0.5)/2n as n goes to infinity (which is the series you wrote out just now)

But you reach X because as the rubber band expands then the robot’s position from X also expands, so that the % of journey completed remains constant through expansion

ah, I thought it was on a rubber band like a line, not in a rubber band like a circle.