Riddle #5:

You've got it, M.  I think the O.R. is referencing the earth, but for any size globe with circumference greater than 2 miles the answer is the same: there will be a latitude in the southern hemisphere whose length (the circumference of that slice of the globe) will be one mile.  All points on the latitude one mile north of that are solutions.  Rinse and repeat for a 1/2 mile latitude, a 1/3 mile latitude, etc.

For globes whose circumference is two miles or less the answer is 0, because at 2 miles "one mile south" puts you at the south pole and traveling east is not possible, and at less than 2 miles traveling "one mile south/north" is not possible.

NewlyIdle wrote:

Riddle #5:

For globes whose circumference is two miles or less the answer is 0, because at 2 miles "one mile south" puts you at the south pole and traveling east is not possible, and at less than 2 miles traveling "one mile south/north" is not possible.

Yeah - I was rethinking my answer and realized this..

You've got it, M.  I think the O.R. is referencing the earth, but for any size globe with circumference greater than 2 miles the answer is the same: there will be a latitude in the southern hemisphere whose length (the circumference of that slice of the globe) will be one mile.  All points on the latitude one mile north of that are solutions.  Rinse and repeat for a 1/2 mile latitude, a 1/3 mile latitude, etc.

I didn't really get it; you did.  But I was getting close. I was still trying to deal with similar latitudes in the Northern Hemisphere (which doesn't work because the latitudinal length will always be too large), but I think I would have eventually figured it out.

So these plus the North Pole should do it, right?

I have long ears and hop when I travel, but require no sustenance. What am I?

NewlyIdle wrote:

Riddle #5:

For globes whose circumference is two miles or less the answer is 0, because at 2 miles "one mile south" puts you at the south pole and traveling east is not possible, and at less than 2 miles traveling "one mile south/north" is not possible.

that's not accurate. 1 mile south on a 2mi circumference puts you at the 'equator'

you have one spot at the north pole that will always be true for a globe with circumference > 1mi; and infinite spots when circumference is > 2mi - based on your other explanation:

I think the O.R. is referencing the earth, but for any size globe with circumference greater than 2 miles the answer is the same: there will be a latitude in the southern hemisphere whose length (the circumference of that slice of the globe) will be one mile.  All points on the latitude one mile north of that are solutions.  Rinse and repeat for a 1/2 mile latitude, a 1/3 mile latitude, etc.

weathertop wrote:

NewlyIdle wrote:

Riddle #5:

For globes whose circumference is two miles or less the answer is 0, because at 2 miles "one mile south" puts you at the south pole and traveling east is not possible, and at less than 2 miles traveling "one mile south/north" is not possible.

that's not accurate. 1 mile south on a 2mi circumference puts you at the 'equator'

I think NI is correct.

With a 2mi circumference, you only have to travel 1/2 mi from a pole to reach the equator..

..and travelling 1 mile south starting at the North Pole puts you on the South Pole, in which case you can't go east because there is no east. NI correctly stated that a 2mi circumference has no correct solutions.

yeah, my bad. i was thinking semi-circumference - only taking in half of it.

so the correct answer is:
you have one spot at the north pole that will always be true for a globe with circumference > 2mi; and 'infinite' spots when circumference is > 4mi.

Amidon37 wrote:

From a joke book I had as a kid - not sure if the riddle is well known or not, but I remember it fondly -

 

What can go up a chimney down, but can't go down a chimney up?

I want to know the answer to this one.

not quite -- there's one answer -- there are infinite spots at >2miles and no spots at exactly 2mi

Take the case where the circumference is 2 1/2 miles

While there is no latitude whose length is 1 mi that has a legitimate starting point 1 mile north, there is a latitude whose length is a reciprocal of some multiple of 1 mile.  I.e.  1/100 of a mile.

In this case you travel 1 mile south to that latitude -- circle the earth 100 times, then travel north to your starting destination.

This one is for the mathematicians among you:  

You have 12 balls identical in size and appearance but 1 is an odd weight (could be either light or heavy). 

You have a set scales (balance) which will give 3 possible readings: Left = Right, Left > Right or Left < Right (ie Left and Right have equal weight, Left is Heavier, or Left is Lighter). 

You have only 3 chances to weigh the balls in any combination using the scales. Determine which ball is the odd one and if it's heavier or lighter than the rest. How do you do it?

Ozyman wrote:

Amidon37 wrote:

From a joke book I had as a kid - not sure if the riddle is well known or not, but I remember it fondly -

 

What can go up a chimney down, but can't go down a chimney up?

I want to know the answer to this one.

It's an umbrella.  It won't fit through a chimney when it's up.

Riddle #5: You got it, and extended it to other sizes of the globe.

For the original question, the correct enumeration is 1 + Inf + Inf

1   - North Pole (obvious)

Inf - All points on the circumference starting 1 mile North of the latitude where the circumference of the globe is exactly 1 mile.

Inf - The infinite set of circumferences (1 mile North of) where going 1 mile East will take you around the globe 2 times, 3 times, 4 times, etc...  Assuming infinite precision, of course.

I always thought of it as 1 + Inf * Inf, as that's how it makes sense in my mind.  But my Math PhD friends at MIT assure me that in this case, Inf + Inf vs. Inf * Inf is a meaningless distinction, but that it's more correct to say 1 + Inf + Inf.  Maybe they are full of crap - but who am I to say?

What do you put  in a toaster?

What do cows drink?

itsnotatumor wrote:

What do you put  in a toaster?

What do cows drink?

Bread.

Water.

Answer my riddle above :)

ratsy wrote:

This one is for the mathematicians among you:  

You have 12 balls identical in size and appearance but 1 is an odd weight (could be either light or heavy). 

You have a set scales (balance) which will give 3 possible readings: Left = Right, Left > Right or Left < Right (ie Left and Right have equal weight, Left is Heavier, or Left is Lighter). 

You have only 3 chances to weigh the balls in any combination using the scales. Determine which ball is the odd one and if it's heavier or lighter than the rest. How do you do it?

This is more of a logic problem. I have been unable to solve it.  I can do it with 9 balls but even there, I'm having trouble distinguishing if the odd ball is heavier or lighter.  There are some cases where I'm sure, but..

M57 wrote:

ratsy wrote:

This one is for the mathematicians among you:  

You have 12 balls identical in size and appearance but 1 is an odd weight (could be either light or heavy). 

You have a set scales (balance) which will give 3 possible readings: Left = Right, Left > Right or Left < Right (ie Left and Right have equal weight, Left is Heavier, or Left is Lighter). 

You have only 3 chances to weigh the balls in any combination using the scales. Determine which ball is the odd one and if it's heavier or lighter than the rest. How do you do it?

This is more of a logic problem. I have been unable to solve it.  I can do it with 9 balls but even there, I'm having trouble distinguishing if the odd ball is heavier or lighter.  There are some cases where I'm sure, but..

It took me the better part of a year to finally figure this out.  Don't give up too quick!

Are you the Targus Atilla?

AttilaTheHun wrote: I have long ears and hop when I travel, but require no sustenance. What am I?

My first thought was the energizer bunny, then popcorn, then neurons, then thought, "Do quarks have ears?" But, I'm going to go with an anthropomorphic personification. Final Answer.

AttilaTheHun wrote: I have long ears and hop when I travel, but require no sustenance. What am I?

Some kind of radio signal or  network?  They can use 'rabbit ear' antennas.  Each bounce or re-transmission is referred to as a hop.

Either that or Zombie Bunnies.

Everybody wins!  The answer was shoelaces but probably not the most well-worded riddle...