If ‘MUD’ is written as ‘FYS’ and ‘BAT’ is written as ‘VEH’, then how is ‘HAN’…

Concept

In a letter-coding problem, each letter of the original word is moved forward or backward in the alphabet by a fixed pattern of steps. When a code is required to be a "meaningful word", the shifted letters are first found, and then arranged so that they spell a valid dictionary word; the position order may change but the set of letters does not.

Rule discovered

Shift the three letters forward by +6, +4 and +2 places respectively (A=1, B=2, ... Z=26, wrapping after Z), then rearrange the resulting letters into a meaningful word.

Verifying the rule on the given pairs

1. MUD: M(13)+6 = S, U(21)+4 = Y, D(4)+2 = F, giving the letters {S, Y, F}; arranged as the given code FYS.

2. BAT: B(2)+6 = H, A(1)+4 = E, T(20)+2 = V, giving the letters {H, E, V}; arranged as the given code VEH.

Application to HAN

1. H(8)+6 = N

2. A(1)+4 = E

3. N(14)+2 = P

4. The shifted letters are {N, E, P}.

5. Among the arrangements of N, E and P, only PEN is a meaningful English word, so the required code is PEN.

Cross-check

The set {N, E, P} matches the letters in PEN exactly, and PEN is the single dictionary word formed from them, satisfying the condition that the code must be a meaningful word.