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 whose house is located at L, needs to visit the post office as well as the bank. What is the minimum distance (in m) he has to walk starting from his residence and returning to his residence after visiting both the post office and the bank?

The correct option is NOTA (None of the Above).

To determine the minimum walking distance for the resident starting at residence L, visiting both the post office (at P) and the bank (at B), and returning to L, we can first establish a coordinate system based on the given dimensions in the diagram:

Let the point P be at the origin (0, 0).
Using the distances provided:
- OP = 150 m ⇒ O is at (150, 0)
- ON = 300 m ⇒ N is at (450, 0)
- MN = 300 m ⇒ M is at (750, 0)
- ML = 400 m ⇒ L is at (750, 400)
- EL = 200 m ⇒ E is at (750, 600)
- DE = 400 m ⇒ D is at (750, 1000)

Using this rectangular grid layout, the coordinates of the key points are:
- P (Post Office) = (0, 0)
- O = (150, 0)
- N = (450, 0)
- M = (750, 0)
- L (Residence) = (750, 400)
- K = (450, 400)
- J = (150, 400)
- I = (0, 400)
- E = (750, 600)
- F = (450, 600)
- G = (150, 600)
- H = (0, 600)
- D = (750, 1000)
- C = (450, 1000)
- B (Bank) = (150, 1000)
- A = (0, 1000)

Next, we calculate the lengths of the diagonal walkways:
1. Walkway IG between (0, 400) and (150, 600):

$$\text{IG}=\sqrt{{(150-0)}^2+{(600-400)}^2}=\sqrt{{150}^2+{200}^2}=250\text{ m}$$

$$\text{OK}=\sqrt{{(450-150)}^2+{(400-0)}^2}=\sqrt{{300}^2+{400}^2}=500\text{ m}$$

Now, we evaluate the shortest paths between the destinations:

Leg 1: L to P (Residence to Post Office)
- Path: L → K → O → P
- Distance: LK + KO + OP = 300 + 500 + 150 = 950 m.

Leg 2: P to B (Post Office to Bank)
- Path: P → I → G → B
- Distance: PI + IG + GB = 400 + 250 + 400 = 1050 m.

Leg 3: B to L (Bank to Residence)
- Path: B → G → F → K → L (or B → C → D → E → L)
- Distance: BG + GF + FK + KL = 400 + 300 + 200 + 300 = 1200 m.

Summing the minimum distances for the complete loop:

$$\text{Total Distance}=950+1050+1200=3200\text{ m}$$

Based on the calculated minimum loop distance of 3200 m, the correct choice is NOTA because the official answer key specifies "None of the Above" (NOTA).