bonanova

To what class of numbers do those that are infinitesimally small belong?

Title is fav quote by Kipling, on equality. How about you on the same subject, but mathematically, not philosophically: Can two numbers x and y written in decimal expansion differ in every decimal place, yet be equal?

The difficulty with this approach is that if the students do as the OP requires, the student who made your additional assumption of fairness would pick chair #2.

This is a variant of the Unexpected Hanging paradox described by Martin Gardner and others. It was posted in this forum here: And here: Please read these threads, and post any new thoughts here.

The meandered without a definitive answer. Since I contributed a question that that thread, I'll answer it after answering the OP. jim gives the same answer above.

Here's a collection of clues amassed so far...

Just a couple things to arrange, in principle. It would have to be very level, no wind currents, loud talking, foot stomping, and ice made from an inviscid liquid. That should do it. Oh, to eliminate that troublesome coriolis effect, stop the Earth from rotating for about an hour and a half. All most as much fun to think of what things would disturb the experiment. I'm sure there are others. Nice idea.

fabpig, you're right on. The same equations govern low/earth orbits Just as EventHorizon showed the tunnel doesn't need to be an Earth diameter. A surprising, non-intuitive result. And now that this wonderful number is out of the bag, so to speak, Anyone want to take a guess what all the rows and major diagonals of a 3 x 3 x 3 magic cube [using the numbers 1-27] sum to?

I'm thinking it would be hard to improve on that. Nice.

Hi jim, welcome to the Den. Sorry I didn't see your post earlier. Yes, that question would do it. I had in mind the idea inthe previous post, and now three others have been given. Nice!

Yeah, both of those questions work. Nice! Are there others? If Jaimie's response is taken as a clue, for example.

I just thought of a positive integer less than 4 said Alex to his friends Davie and Jaimie last night at Morty's while idly tossing darts in the back corner of the room. It was a slow night, and Alex loved to keep things interesting, as best he could. Now if I were to give you two questions of the standard Yes/No variety, I have no doubt that even you two geniuses could deduce what my number is. So, I'll raise the challenge a bit, and buy the next round of beer, if you can tell me my number - with absolute certainty - after asking me a single Yes/No question. Davie didn't even bother to stroke his beard. Can't be done, pure and simple. A waste of time, If you ask me, agreed Jaimie. Neither of them noticed the twinkle in Alex's eye as he continued to reel them in. All right, I'll turn it around. You pick the number and I'll ask the question. And if you can't answer it, you'll have to say so. But it will cost you to play. If I get it right, with certainty, you buy. If I get it wrong, I'll buy. Either of you up to that? Jaimie Just walked away, muttering something quietly about complexity. This time Davey did stroke his beard and after a minute said, OK, you're on. Who bought the next round?

A fact I was not aware of. I was hitch-hiking through the galaxy instead.

Well they're OK I guess, but their product doesn't explain life, etc.

It would be an interesting scheme to simulate.

Suppose you dug a frictionless tunnel straight through the Earth. Then suppose you jumped into the tunnel. Ignoring the inconvenient fact that this might turn you into a large cinder, and ignoring wind drag [you evacuated the tunnel and encapsulated yourself] when would you next see the light of day? Would it matter whether the tunnel went through the Earth's center? To keep it simple, assume the Earth is spherical and homogeneous. Except of course for the hole you dug through it. Assume if you like that gravity's acceleration at the surface is 9.8 m/s2, and Earth's circumference is 40 million meters.

Rookie would prob reinstate you. PM him. Eternal editing is cool.

And I'm so glad it is. 7 and 6 are two of my fav numbers.

Good point. In real life there would've 23 funerals before the guaranteed solution had run its course.