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The above is a schematic diagram of walkways (indicated by all the straight-lines) and lakes (3 of them, each in the shape of rectangles - shaded in the diagram) of a gated area. Different points on the walkway are indicated by letters (A through P) with distances being OP = 150 m, ON = MN = 300 m, ML = 400 m, EL = 200 m, DE = 400 m.
The following additional information about the facilities in the area is known.
1. The only entry/exit point is at C.
2. There are many residences within the gated area; all of them are located on the path AH and ML with four of them being at A, H, M, and L.
3. The post office is located at P and the bank is located at B.
One resident takes a walk within the gated area starting from A and returning to A without going through any point (other than A) more than once. What is the maximum distance (in m) she can walk in this way?
Correct Answer: 5100
Counter to the first question, we should minimize the use of those hypotenuse walkways as they reduce the distance we travel.
But after some trial and error, one would find that taking the GI walkway actually lets us travel a greater distance overall.Â
The longest route possible can be visualised as follows:
Walkways of lengths 400m are covered 6 times: AH, ED, ML, KN, OJ, IP
Walkwys of length 300m are covered 6 times: JK, NM, DC, CB, LK, FE
Walkways of length 200m covered 1 time: KF
Walkways of length 150 m covered 3 times: BA, HG, PO
Walkways of length 250 m covered 1 time: GI
Giving total length to be 2400+1800+200+450+250 = 5100
Therefore, 5100 is the correct answer.Â
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