Select the option that is related to the fifth letter-cluster in the same way…

Concept: In a letter-cluster analogy the code is built from the source word by one fixed operation applied in two parts: a re-ordering of the letters of the word, followed by a shift of each letter through the alphabet. The shift can be the same at every position, or it can itself follow a pattern that changes with the position. A rule counts as established only when a single operation reproduces every pair that is given; a rule fitted to one pair alone has not yet been tested.

Application: Work with alphabet positions A = 1, B = 2, ..., Z = 26, and let a shift that passes Z wrap round to A.

1. Reverse the first source word. SCOOTER read from its last letter to its first is RETOOCS.

2. Line RETOOCS up against its code SGWSTIZ and measure each step: R(18) to S(19) is +1, E(5) to G(7) is +2, T(20) to W(23) is +3, O(15) to S(19) is +4, O(15) to T(20) is +5, C(3) to I(9) is +6, S(19) to Z(26) is +7.

3. The step grows by one at each successive position, so the candidate rule is: reverse the word, then advance the letter standing at position n of the reversed word by n places.

4. Test that candidate on the second pair. AEROPLANE reversed is ENALPOREA, and E(5)+1 = F, N(14)+2 = P, A(1)+3 = D, L(12)+4 = P, P(16)+5 = U, O(15)+6 = U, R(18)+7 = Y, E(5)+8 = M, A(1)+9 = J, giving FPDPUUYMJ, which is exactly the code supplied. One operation now reproduces both pairs, so the rule is established.

5. Apply the established rule to HELICOPTER, which reversed is RETPOCILEH.

Reading the results down the last column gives SGWTTIPTNR, so HELICOPTER : SGWTTIPTNR.

Cross-check: Each near-miss cluster comes from dropping one half of the rule, and each one breaks on a pair that was already supplied.

• RETPOCILEH is the reversal on its own, with no letter advanced. Under that reading SCOOTER would be coded RETOOCS, not the SGWSTIZ that was given.

• SFUQPDJMFI advances every reversed letter by exactly one place. Under that reading SCOOTER would be coded SFUPPDT, not the SGWSTIZ that was given.

• SGWTTIPLEH stops the growing advance after the seventh letter. Under that reading AEROPLANE would be coded FPDPUUYEA, not the FPDPUUYMJ that was given, because its eighth and ninth reversed letters E(5) and A(1) must still carry the +8 and +9 steps to M and J.

• A last check on the tail: the tenth reversed letter H(8) has to advance +10 to R(18), and SGWTTIPTNR is the only cluster here that both begins SGWTTIP and closes on R.