In a certain code ‘FORGIVE’ is written as ‘DPPHGWC’. How would ‘REQUEST’ be…

Concept: In alphabet-shift coding puzzles, each letter of a word is replaced by another letter obtained by moving a fixed number of places forward or backward through the alphabet, and this shift amount can alternate in a repeating pattern across consecutive letters. The coding rule is found by comparing each letter's alphabet position in the original word with the corresponding letter of the given code, position by position.

Application: deriving the rule from FORGIVE → DPPHGWC, then applying it to REQUEST.

1. Assign each letter its position in the alphabet (A=1, B=2, ... Z=26).

2. Compare each letter of FORGIVE with the corresponding letter of DPPHGWC: F(6)→D(4) is -2; O(15)→P(16) is +1; R(18)→P(16) is -2; G(7)→H(8) is +1; I(9)→G(7) is -2; V(22)→W(23) is +1; E(5)→C(3) is -2.

3. Identify the pattern: the shift alternates -2, +1, -2, +1, -2, +1, -2 across the seven letters.

4. Apply the same alternating shift to REQUEST (R, E, Q, U, E, S, T): R(18)-2=P(16); E(5)+1=F(6); Q(17)-2=O(15); U(21)+1=V(22); E(5)-2=C(3); S(19)+1=T(20); T(20)-2=R(18).

5. Combine the shifted letters in order to get the coded word: PFOVCTR.

Cross-check: comparing the derived code PFOVCTR against each of the three specific letter arrangements offered shows no exact letter-for-letter match, confirming that the alternating shift rule, applied consistently, does not produce any of them.

Therefore, the code for REQUEST is PFOVCTR, which is not listed among the given options, so the correct answer is 'None of these'.