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# Fence

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Two hundred fence posts are to be placed into the ground in a straight line, 2m apart. The fence posts are stacked in a pile along this same line, 2 m from the position of the first post to be put in. Maybell is going to put inthe posts one at a time in order, and each post she puts in is farther away from the pile. Maybell can only carry one post at a time, and so she always walks back to the pile to getthe next post. If Maybell starts at the pile, how many kilometers must she walk to finish the job?

Feb 3, 2018

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Note that to put in the first post and return, she walks  2 * 2 m  =  4m = 4 (1) m

And  the total distance she walks to put in the second post is    2 * 4m  =  8m  = 4 (2) m

And the distance she walks to put in the third post is  2 * 6m  = 12m  = 4 (3) m

So....to put in  N posits...it appears that the total distance waked is

4 ( 1  + 2 + 3 + ......+  N )  m

And the sum of the first positive N  integers can be expressed  as    (N /2) * (N + 1)

So...the total distance she walks (in meters)   for 200 posts is :

4 [ (200/2) (201) ]   =  2 (200)(201) = 80, 400 m

Converting this to kilometers, she walks   80,400 / 1000  =

80.4  km !!!      that's a lot of walking  !!!

Feb 3, 2018