Hard Riddle #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 of 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.

Can't you think of something simpler?!

@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 of 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.

IS THIS A RIDDLE OR A MATH QUESTION?

Explain your answer with math or logic.
Just trying to solve it ok?
-Rubber band circumference = pi*diameter =1meter
-When growing at rate of 1 meter/s the diameter grows at rate of 1/pi per second.
-Diameter is inside the rubber band.
0.5>1/pi is true

Answer is yes, because robot velocity is faster than the diameter velocity.

No. Because the robot can fall when the rubber band is growing.

@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 of 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.
No answer,circumfrence cant be rational number

Assuming you mean that the circumference is increasing by 1 m/s:

imagine the rubber band as one straight line, the start line is point X and the finish line is also point X. the robot moves 0.5 m forward, then the straight line expands by 1m, so you would think that the robot can never make it, but the crucial point is that as the straight line increases in length, the robot is dragged along with it, so it is the same % way through the line as it was before.

struggling a bit with the maths so I will just see what happens after a few turns, with the notation (robot distance, total line length)

(0,1) (0.5,1) (1,2) (1.5,2) (2.25,3) (2.75,3) (3.66666666, 4) (4.1666666,4)

so he can actually make it, now that i think of it we can think of this as a fraction sum, ie 0.5/1 + 0.5/2 + 0.5/3 + 0.5/4 + 0.5/5...... representing the total fraction of the journey completed (the key point is that the rubber band expansion does not affect this fraction of journey completeness, as the robot is dragged along with the expansion.) This is half the harmonic series, so he will completely infinitely many laps of X
hopefully i didn’t misunderstand the wording or mess up

After rescaling, the problem is exactly the same as a robot moving at speed 0.5/t on a rubber band of constant circumference 1 (t starting at 1)
Now, because the integral from 1 to infinity of 0.5/t diverges, the robot will be able to make infinitely many loops, as Calby said.

This problem is not very well defined:

@TakeThePawnOrLose said in #1:

This rubber band is growing at a rate of 1m/s

One needs to state where this growing occurs: if the growing is distributed evenly so that the point "x+1m" at t=0 will be at 2m at t=1 and x+0.5m at t=0 will be at x+1m at t=1, then the solution of @CalbernandHowbe at #8 is correct.

If the growing only occurs at one point it depends: if this point is at x, so that it is "behind" the moving robot then the robot will - regardless of the growing - reach x again after 2 seconds because the rubber band before it always stays at 1m length.

If the growing happens "in front" of the robot it will never reach X again, because the distance still to be traveled increases at a rate of 1m/s whereas its movement decreases this distance at a rate of 0.5 m/s, giving a net increase of 0.5 m/s.