In a certain coded system of directions, the direction name South-East is replaced by North and the direction name North-East is replaced by West, and all other directions are renamed in the same cyclic pattern.\nAccording to this scheme, which direction name will be used in place of South?

Introduction / Context:
This problem belongs to the direction sense and coding category, where normal compass directions are renamed according to a given rule. Instead of moving a person on a map, we are told that specific directions are changed into new labels. Our task is to understand the pattern of renaming and then apply the same pattern to find what the original direction South will be called in this new coding system. Such questions primarily test logical reasoning and understanding of cyclic arrangements of the eight principal directions.

Given Data / Assumptions:

• There are eight standard directions: North (N), North-East (NE), East (E), South-East (SE), South (S), South-West (SW), West (W) and North-West (NW).
• In the new coded system, South-East is changed to North.
• In the same coded system, North-East is changed to West.
• The phrase “and so on” implies that the same cyclic rule applies to all remaining directions consistently.
• We assume that the renaming follows a fixed step of rotation around the compass.

Concept / Approach:
To solve this, we list the eight directions in their natural clockwise order and try to interpret how the coding rule shifts one direction to another. By observing how South-East (SE) becomes North (N) and North-East (NE) becomes West (W), we can determine the shift in terms of positions along the circle. Once the exact shift is identified, we apply the same shift to South (S) to find its new name. This is essentially a problem of modular arithmetic on a circular arrangement.

Step-by-Step Solution:
Step 1: Write the eight directions in order: N, NE, E, SE, S, SW, W, NW. Step 2: Assign position numbers for convenience: N(0), NE(1), E(2), SE(3), S(4), SW(5), W(6), NW(7). Step 3: According to the code, SE (position 3) is renamed as N (position 0). This is a shift of -3 positions or equivalently +5 positions modulo 8 (because 3 + 5 = 8, which wraps to 0). Step 4: Check the second mapping: NE (position 1) is renamed as W (position 6). This is also a shift of +5 positions (1 + 5 = 6), confirming the pattern. Step 5: Apply the same +5 shift to South (S), which is at position 4. We compute 4 + 5 = 9; modulo 8, this is 1, which corresponds to North-East (NE). Step 6: Therefore, South will be called North-East in this coded system.

Verification / Alternative check:
Another way is to visualize the directions on a circle and imagine that each direction is being relabelled by rotating five steps clockwise. Moving from SE to N involves “backing up” three positions or equivalently moving forward five positions. If we keep jumping five directions clockwise, NE indeed maps to W, and applying the same jump from S lands us on NE. This graphical intuition matches the position-counting method, confirming that North-East is the correct coded name for South.

Why Other Options Are Wrong:
South-West would require a different rotation step and does not match the observed mappings from SE and NE. South-East clearly cannot be the code for South because SE already has its own new name. North-West also does not follow the +5 shift pattern from S. East is similarly inconsistent with the shift that maps SE to N and NE to W. Only North-East preserves the same rotational behaviour for all the given cases.

Common Pitfalls:
A frequent mistake is to assume that directions are simply reversed or that North is always swapped with South, East with West, and so on. Here, however, the problem specifies only two mappings and asks the solver to infer the exact cyclic rule. Another pitfall is miscounting the steps around the circle or mixing up clockwise with anticlockwise movement. Writing the directions down in a clear ring and marking the step size prevents such errors and makes the pattern much easier to see.

Final Answer:
Under this renaming system, the direction South will be referred to as North-East.