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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>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.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>A hiker walks north 4 km, turns and walks east 3 km. How far is the hiker from the starting point?<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>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.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>So here’s the really cool question: assuming the north pole trick, what is the farthest she could end up from the start?<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>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.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>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.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>spike<o:p></o:p></p></div></body></html>