## Sunday, 2 September 2012

### Hugging the World

This is one of those puzzles to which the answer seems counter-intuitive.

One day, Bill Gates decides that he wants to “hug the world”.  The way he is going to do it is to arrange Ethernet cable that is long enough to wrap all the way around the world.  He comes to you to calculate the length of cable required.

For a host of very good reasons, you make the assumption that Bill wants this cable to be at sea level at the equator and you calculate a very nice accurate figure.  When you present this figure to Bill, he questions you about the poles.

“Poles? I went around the equator,” you say.

Bill then patiently explains that while you were right about the equator, he obviously wants the cable to be suspended one meter above sea level, so it won’t get wet.  To achieve that you will need to use the fourty million poles that Bill has stacked up in the backyard of one of his mansions.  (Note that Bill so loves the world that he also willing to pay for certain countries to be leveled to keep the cable at precisely one meter about sea level.)

How much more Ethernet cable will now be needed, over and beyond the figure you calculated?  (If you need help, it might help to know that the circumference of the Earth at sea level at the equator is 40,075.016686km.)

I’ll provide an answer in a few days – if no-one works it out in the meantime.

1. If C=40,075.016686, then the radius that we are talking about is C/2pi (units in km). So can't we just add 1 meter to that to get our new radius C/2pi+.001, and then to get the new circumference we just multiply by 2pi again to get C+.002pi.

It seems we only need about 6 extra meters of cable. Have I oversimplified things somewhere? That doesn't seem right.

2. Hi Hausdorff,

It's counter-intuitive as I said. It's not overly difficult to calculate, as you have shown. The answer - which is 2pi metres - is exactly right but doesn't seem right. It doesn't seems to match up if when adding 40 million one-metre poles to the scenario, you only add slightly less than 6.3m of length to the cable.

3. That's great. I love things that are counter-intuitive and yet easy to calculate. It really shows us that we need to take our intuition with a grain of salt

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