Take the tour ×  A man moves 1km east, 2km north, 3km west, 4km
south, 5km east, 6km north, 7km west and so on until he travels
total of 300km. So what will be the distance from origin?
share|improve this question add comment  2 Answers  up vote 3
down vote accepted  To travel 300 km, he would need to take 24
"steps".  For every 4 steps, he travels $2\sqrt{2}$ km south
west. He will do this 6 times, so the answer is $12\sqrt{2}$ km
share|improve this answer add comment  As $1+2+ \cdots +n =
\frac{n}{2} (n+1) $, and $300 = 12 \times 25 $, the final
movement after 300km is 24km. This is in the direction south,
which is easily deduced.  The total distance moved north is $2 +
6 + \cdots + 22$. This is a simple arithemetic series, the sum
of which is 72.  By the same method, the total distance moved
east is 66, south is 84, and west is 78.  Therefore, the total
horizontal displacement is 12, and the total vertical
displacement is 12.  So, the displacement from the origin =
$\sqrt{12^2 + 12^2} =12\sqrt{2} $.  sha