In a certain code language ‘KEYBOARD’ is written as ‘FMGADQCT’. How will…

Concept: A shift-and-rotate letter code is built in two independent stages. First, every letter of the word is replaced by the letter a fixed number of places ahead of it in the alphabet, wrapping from Z back to A. Second, the whole block of coded letters is rotated by a fixed number of positions, so a letter that entered at one place leaves at another. Such a code is defined by exactly two parameters — the size of the alphabetical shift, and the size and direction of the rotation — and both must be read off the given sample before any new word is coded.

Application: The sample pair KEYBOARD → FMGADQCT fixes both parameters.

1. Shift each letter of KEYBOARD two places forward in the alphabet: K → M, E → G, Y → A (Y wraps past Z back to A), B → D, O → Q, A → C, R → T, D → F. The shifted block is M G A D Q C T F.

2. Rotate that block one place to the right, which carries its last letter F to the front: F M G A D Q C T. This reproduces the code given for KEYBOARD, so the shift is two places forward and the rotation is one place to the right.

3. Apply the same shift to TOUCHPAD: T → V, O → Q, U → W, C → E, H → J, P → R, A → C, D → F. The shifted block is V Q W E J R C F.

4. Rotate that block one place to the right, carrying F to the front: F V Q W E J R C. This is how TOUCHPAD is written in the code.

Cross-check: Run the rule backwards on FVQWEJRC. Moving its leading F to the end undoes the rotation and gives V Q W E J R C F; shifting each of those letters two places back gives T, O, U, C, H, P, A, D — the original word TOUCHPAD. The same reverse check turns FMGADQCT back into KEYBOARD, so both parameters are confirmed.

Contrast: The near-miss strings break the rule at identifiable letters.

• FVQWEJSC follows the rule for its first six letters but carries S in the seventh place; the seventh coded letter comes from P, and P shifted two places forward is R, not S.

• FVQWEISB closes with I, S and B, whereas the letters H, P and A that feed those three places give J, R and C under a two-place forward shift.

• FUQEBSJR agrees with the rule only at its first and third letters; its second letter U is not the two-place shift of T, and its fourth letter E is not the two-place shift of U.