If HOBBY is coded as IOBY and LOBBY is coded as MOBY; then BOBBY is coded as

Concept

In alphabet-based coding, the code word is produced from the original word by one fixed rule. Recover that rule by aligning the two words letter by letter: a difference in length signals a structural operation, such as writing a repeated pair of letters only once, while a difference in identity signals a positional shift along the alphabet. A rule may be accepted only after it reproduces every pair given in the question.

Applying it here

1. HOBBY has five letters while its code IOBY has four, so exactly one letter is lost when the rule is applied.

2. HOBBY contains the doubled pair BB and IOBY contains a single B, so the doubled letter is written only once; HOBBY therefore reduces to H, O, B, Y.

3. Compare H, O, B, Y with I, O, B, Y: the last three letters are unchanged and only the first letter moves, from H to I, that is one place forward in the alphabet.

4. The rule is therefore: write the doubled pair as a single letter, and advance the first letter by one place in the alphabet.

Cross-check

Test the rule on the second pair supplied in the question. Writing the doubled B of LOBBY once gives L, O, B, Y, and advancing the first letter L by one place gives M, which produces MOBY, exactly the code stated. The rule reproduces both given pairs, so it can be trusted.

Applying the same rule to BOBBY: writing the doubled B once gives B, O, B, Y, and advancing the first letter B by one place gives C. The code for BOBBY is therefore COBY.