In the following series, only one letter-cluster is incorrect. Select the…

Concept

A letter-cluster series is governed by two rules that must both hold. The internal rule links the letters inside a single cluster, and the step rule fixes how one cluster moves to the next through the alphabet. To test such a series, convert every letter to its alphabet position (A = 1, B = 2, ..., Z = 26) and then check both rules on every cluster.

Application

Written with alphabet positions, the printed series reads:

1. Convert every printed cluster to alphabet positions, as in the table above.

2. Read the internal rule from PLP, MIM, JFJ and GCG: in each of them the last letter repeats the first letter, and the middle letter stands 4 places before the first letter.

3. Read the step rule from the first letters of those clusters: 16, 13, 10, 7 - a constant fall of 3. The fifth cluster must therefore open at position 7 - 3 = 4, the letter D.

4. Test the printed fifth cluster, CYF: it opens at position 3 (C) instead of 4 (D), and its last letter F (6) does not repeat its first letter C (3). Both rules break, so CYF is the incorrect letter-cluster.

5. Continuing both rules gives the cluster that belongs in that place: D as the outer letters, and a middle letter 4 places before D, which runs past A and comes back to Z - that is, DZD.

Cross-check

Apply both rules to each remaining printed cluster: PLP (16, 12, 16), MIM (13, 9, 13), JFJ (10, 6, 10) and GCG (7, 3, 7) all repeat their first letter at the end, all place their middle letter 4 places before their first letter, and their first letters fall by exactly 3 each time. All four are consistent with both rules, so exactly one cluster of the series is incorrect, as the question states.