Directions: In a certain code, BADMINTON is written as DBANIMNTO, in that…

In many coding-decoding puzzles, the coded word is not produced by one single named operation applied uniformly to the whole word (such as 'reverse the whole word' or 'shift every letter by one'). Instead, the given word is split into equal-sized groups of letters, and each group is rearranged in its own specific way. Once the group-by-group rearrangement used in the example is identified, the exact same set of operations — applied to the corresponding groups — must be used to encode any new word of the same length.

BADMINTON has nine letters, so it splits into three groups of three: BAD, MIN, TON. Comparing each group with its given code shows exactly how it is rearranged:

1. BAD to DBA: the last letter of the group moves to the front (B, A, D becomes D, B, A).

2. MIN to NIM: the group is reversed outright (M, I, N becomes N, I, M).

3. TON to NTO: the last letter of the group again moves to the front (T, O, N becomes N, T, O).

So the first and third groups have their last letter shifted to the front, while the middle group is fully reversed. AEROPLANE also has nine letters and splits into AER, OPL, ANE, so the same three operations carry over group by group:

1. AER (shift last letter to front): A, E, R becomes R, A, E, giving RAE.

2. OPL (reverse): O, P, L becomes L, P, O, giving LPO.

3. ANE (shift last letter to front): A, N, E becomes E, A, N, giving EAN.

Joining the three coded groups gives RAE + LPO + EAN = RAELPOEAN.

Cross-check: applying the same three operations to BADMINTON's own groups (BAD, MIN, TON) reproduces DBA, NIM, NTO — exactly the given code DBANIMNTO — confirming the operations were identified correctly before carrying them over.

So AEROPLANE is coded as RAELPOEAN.