[ExI] how far can she go?

[spike]

It was a time joke, on me.  In an offline discussion I was relating a story
that happened to me 35 years ago, and I just now got it.  It was an IQ test
question, not multiple choice, it was administered by a live psychologist.

 

A hiker walks north 4 km, turns and walks east 3 km.  How far is the hiker
from the starting point?

 

Simple question, answered instantly, 5 km.  But then I realized, the hiker
could start 4+3/2pi km from the north pole.  Then she could turn east, walk
a full circle always walking east for 3 km and end up right where she turned
east, 4 km from where she started.  As far as I know, there is no way on
flat ground she could end up any closer than 4 km.

 

So here's the really cool question: assuming the north pole trick, what is
the farthest she could end up from the start?

 

It's a crazy difficult answer to what looks like an easy question.  All this
time, a cool calculation was waiting for me to discover it.

 

If you give up, I found the answer.  If I did it right, it isn't an integer
or an integer multiple of pi.  Try it first before you ask what I got, good
luck.

 

spike

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