Math problem : 2 objects on an infinite axis

[deuce_bg]

hi everybody , I've been struggling for some time now with this math problem , I still can't come up with a resolution without assume there's an end on the infinite axis :hyper: It goes like this :

There are 2 objects placed on random positions on an infinite axis . Let's say they're robots having built-in algorythm alright and they have exactly the same built-in algorythm . They can do the following . Move a step left , Move a step right , place a flag , check for a flag . That's pretty much it .

The goal is - the robots to meet on the axis eventually .

I fugire checking for a flag can mean that the robot can change it's moving direction which is the key for the goal - if for example the right robot finds one of the left's flags while going left and then switch direction to right and find one of it's own flags ... that's so far I have figured it out . Still as I can see there should be restriction for the axis or ... I don't know .

help please :steering:

[TheBigDog]

Any more information than that?

 

Bill

[snark1100]

the problem is, that when you randomly drop them on the axis, they will land an infinite number of steps away from each other with probablity 1, and so, even if they both start to move towards each other, they will need to take an infinite number of steps to meet.

[TheBigDog]

the problem is, that when you randomly drop them on the axis, they will land an infinite number of steps away from each other with probablity 1, and so, even if they both start to move towards each other, they will need to take an infinite number of steps to meet.

I think that when you drop the two flags on the infinite axle they will be a finite distance from each other. But both will still be an infinite distance from either end. That may be part of the answer, but I suspect we are still missing detail for a solution.

 

Bill

[deuce_bg]

We got it after all . the whole thing is :

the robot follows the flags and if there's no flag places it and goes back.

The whole thing with the infinite axis is that you can't use the end as a way to switch direction . Thanks :steering:

[Pyrotex]

We got it after all . the whole thing is :

the robot follows the flags and if there's no flag places it and goes back.

The whole thing with the infinite axis is that you can't use the end as a way to switch direction . Thanks :steering:

Well, I'm a bit disappointed. I didn't quite understand the original statement of the problem, and now I don't quite understand your statement of the solution.

:hyper: :gift:

oh well. I'm going for some milk and cookies.

[Pyrotex]

Okay, I've got a math problem for you sliderule jockeys. I saw this one when I was a teenager. It took me over an hour to get the answer.

 

You have a sphere of radius R.

You have a drill bit that drills a hole of radius r; r < R.

Using this drill bit, you drill a perfect hole through the center of the sphere. All the way through, creating what we shall call an "annular ring".

You lay the "annular ring" on its side on a flat surface, so that the hole is vertical.

You carefully measure the height of the "annular ring".

 

It is exactly six (6) inches high.

 

What is the exact VOLUME of the annular ring? That is, the VOLUME of the material left over after drilling the hole through the sphere?

 

Now, having said that, I give you a clue: the information above is entirely sufficient to arrive at the correct numerical answer. :steering:

 

In fact, given this clue, you should be able to state the answer without pencil or paper. :hyper:

[Qfwfq]

Good one Pyro, 36*pi! I'll give a thought to the independence on the r/R ratio ASAP but, granted that, it's enough to take the easy way out! :hyper:

 

I think that when you drop the two flags on the infinite axle they will be a finite distance from each other. But both will still be an infinite distance from either end.

No, :steering: Snark was right.

 

The position of the first is clearly irrelevant if the axis extends infinitely both ways. If the probability distribution is uniform when you drop the second, the expectation distance will be half of infinity, which is infinity.

[Qfwfq]

Didn't take long actually, both prop. to the sine of the same angle squared. Or some darn thing like that. :steering:

[Pyrotex]

Good one Pyro, 36*pi! I'll give a thought to the independence on the r/R ratio ASAP but, granted that, it's enough to take the easy way out! ....

Bingo! Good job. And Snark was right.