This article is from the Puzzles FAQ, by Chris Cole email@example.com and Matthew Daly firstname.lastname@example.org with numerous contributions by others.
Title: Cliff Puzzle 13: Ladders to Heaven
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you state otherwise. Thanks, Cliff Pickover
* * *
Consider the following scenario. A standard ladder stretches from each
country on the earth upward a distance equal to the distance from the
earth to the moon.
1. the ladder is made out of a strong metal such as
titanium, which will not break.
2. the ladder is inclined at a very steep angle, 70 degrees, for
3. there is a breathable atmosphere.
4. the people (or teams of people) are allowed to use standard
mountain climbing and camping gear, e.g. ropes, backpacks, etc. but not
sophisticated electrical mechanisms, engines, etc.
5. a reward is given to whomever reaches the top of the ladder
first: 1 million dollars to that person. In addition the country's
national debt is wiped out.
1. Approximate how long it would take a person (or team of people) to
reach the top of the ladder. Days? Weeks? Years?
2. Which country would be the first?
3. Is there any novel method you would suggest to achieve this goal?
4. Is this task impossible to carry out.
Interesting puzzle... Just one question though: Is there a moon,
i.e. is it possible to use the gravitational field of the moon to your
advantage by "falling upwards" once you have reached the point where
the moon's gravity is bigger than the erath's (and do we also assume that
the the climber(s) must survive the fall?? :-) or shall we assume that the
earth is alone in the universe?
Subject: Re: Cliff Puzzle 13: Ladders to Heaven
>1. Approximate how long it would take a person (or team of people) to
>reach the top of the ladder. Days? Weeks? Years?
Note that after you're 22,300 miles from the earth's axis, you get to
"fall" the rest of the way, as long as you don't lose contact with
>2. Which country would be the first?
It has already been pointed out that countries on the equator have an
advantage. I suppose you could consider that countries with a large
national debt have extra motivation. :-)
>3. Is there any novel method you would suggest to achieve this goal?
I would suggest a bicycle-like vehicle clamped to the ladder. By
pulling a light but strong rope on a pulley (perhaps obtained form
the same source as this fantastic ladder material), riders could be
changed fairly quickly, thanks to a crew of brawny pulley-pullers
with a variable-geared linkage to the rope.
For the rider to pull this ever-longer rope seems impossible, but I
think shorter segments could be lifted and linked. Or the ground
crew could help the rider by pulling down rope from a hub of lesser
diameter than the wheels of the vehicle.
>4. Is this task impossible to carry out.
No. I thought it might be impossible to halt at the far end of the
ladder and return, due to centrifugal acceleration, but that
acceleration turns out to be only about 5 cm/s^2.
Matt Crawford email@example.com Java Man
> How do we get food to the people?
I would have the riders change so often that they'd only need some
high-carbohydrate snacks and a couple quarts of fluid. I think the
brawny ground crew could pull up the next rider, with his supplies
and another pulley and segment of rope, at an acceleration of about
0.5 g or better. That would be under 90 minutes for each shift-
change up to the synchronous orbit level.
I haven't figured out yet how to link each new piece of rope that's
pulled up with a rider to the pulley that's at the high point reached
by the previous rider. Linking is easy, but it would be nice to find
a way that lets the next pulled-up rider go from one segment to the
other without interruption. Well, since the sky-buckets at
Disneyland do this trick at each end, I know it can be done.
I didn't know you'd written any books, but it was clear you're
working on one now. Sure, send a list, but I have access to some
on-line catalogs, so maybe I can find them anyway.
> Consider the following scenario. A standard ladder stretches from each
> country on the earth upward a distance equal to the distance from the
> earth to the moon.
> 1. the ladder is made out of a strong metal such as
> titanium, which will not break.
> 2. the ladder is inclined at a very steep angle, 70 degrees, for
> each country.
> 3. there is a breathable atmosphere.
> 4. the people (or teams of people) are allowed to use standard
> mountain climbing and camping gear, e.g. ropes, backpacks, etc. but not
> sophisticated electrical mechanisms, engines, etc.
> 5. a reward is given to whomever reaches the top of the ladder
> first: 1 million dollars to that person. In addition the country's
> national debt is wiped out.
I would imagine that one would be able to fashion a hot air balloon given
condition 4. Also, given condition 3, the hot air balloon would be able
to cover the entire distance. One would then only need to attach a sliding
hookup between the ladder and the balloon and wait.