In a certain code, the word TEACHER is written as VGCEJGT by shifting letters. Using the same code, how is the word CHILDREN written?

Introduction / Context:
This coding and decoding question is based on a Caesar cipher with a forward shift. The word TEACHER is converted into VGCEJGT by moving each letter forward in the alphabet by the same number of positions. Our job is to detect that shift and use it to encode the word CHILDREN in exactly the same way.

Given Data / Assumptions:

• TEACHER is coded as VGCEJGT.
• The same uniform shifting rule applies to all letters.
• We must find the code for CHILDREN.
• The alphabet positions A = 1 through Z = 26 are used implicitly.
• Shifts wrap around if they cross Z.

Concept / Approach:
We examine each pair of corresponding letters in TEACHER and VGCEJGT to determine the size and direction of the shift. If every pair shows the same difference in alphabet positions, that difference gives us the coding rule. Then we apply the same forward shift to each letter of CHILDREN and join the results to obtain the coded word.

Step-by-Step Solution:
Step 1: Find the positions of the letters in TEACHER: T = 20, E = 5, A = 1, C = 3, H = 8, E = 5, R = 18.Step 2: Find the positions of the letters in VGCEJGT: V = 22, G = 7, C = 3, E = 5, J = 10, G = 7, T = 20.Step 3: Compute the difference for each pair. From T to V is +2, from E to G is +2, from A to C is +2, from C to E is +2, from H to J is +2, from E to G is +2 and from R to T is +2. Thus, each letter is shifted two positions forward.Step 4: The coding rule is therefore: replace each letter with the letter two positions ahead in the alphabet.Step 5: Apply this rule to CHILDREN. First write positions: C = 3, H = 8, I = 9, L = 12, D = 4, R = 18, E = 5, N = 14.Step 6: Shift each letter by +2 positions: C → E (3 to 5), H → J (8 to 10), I → K (9 to 11), L → N (12 to 14), D → F (4 to 6), R → T (18 to 20), E → G (5 to 7), N → P (14 to 16).Step 7: Combining these letters, we get EJKNFTGP as the coded form of CHILDREN.

Verification / Alternative check:
To verify, shift each letter of EJKNFTGP two positions backward and confirm that it returns to CHILDREN. E → C, J → H, K → I, N → L, F → D, T → R, G → E and P → N, which reconstructs the original word exactly. This confirms that the rule has been applied correctly and that EJKNFTGP is the correct answer.

Why Other Options Are Wrong:
Options such as EJKNEGTP, EJKNFTGH, EJKNFTPG and EJKNFTGT differ in one or more letters or their order. These differences do not correspond to a consistent shift of two positions from the letters in CHILDREN. Since the cipher is uniform and exact, any option that contains even a single incorrect letter cannot be the correct code.

Common Pitfalls:
Students may miscount the two position shift, especially for letters at the end of the alphabet, or mix up the order of letters when writing the final code. Others guess an answer that looks similar without checking all eight letters. To avoid errors, carefully compute each shift and verify the result by decoding it back to the original word.

Final Answer:
Using a forward shift of two letters in the alphabet, CHILDREN is written in code as EJKNFTGP.