Three-letter blocks with modular +6 shifts (mod 26): ajs, gpy, ?, sbk, yhq Find the missing triplet by tracking each character’s independent progression.

Difficulty: Medium

Correct Answer: mve

Explanation:


Introduction / Context:
This pattern-recognition problem uses blocks of three letters. Each position within the triplet (1st, 2nd, 3rd) follows its own arithmetic progression around the alphabet. We extend those position-wise rules using modular arithmetic (wrapping after Z→A).



Given Data / Assumptions:

  • Triplets: ajs, gpy, ?, sbk, yhq
  • Alphabet indices: a=1, …, z=26.
  • Progressions may wrap around at 26 (modulo 26 arithmetic).


Concept / Approach:
Split the sequence into three independent letter streams: all first letters, all second letters, and all third letters. Determine each stream’s rule (increment per step), then compute the missing letters.



Step-by-Step Solution:

First letters: a(1) → g(7) → ? → s(19) → y(25). The step is consistently +6 mod 26, so missing = m(13).Second letters: j(10) → p(16) → ? → b(2) → h(8). Again +6 mod 26: 10→16→22 (v)→28≡2 (b)→8 (h). Missing second letter = v.Third letters: s(19) → y(25) → ? → k(11) → q(17). With +6 mod 26: 19→25→31≡5 (e)→11 (k)→17 (q). Missing third letter = e.Therefore the missing triplet is m v e.


Verification / Alternative check:


Why Other Options Are Wrong:

  • dmv, oua, qzi each break at least one of the +6 mod 26 streams (first, second, or third letter sequence).


Common Pitfalls:
Trying to relate letters across a triplet instead of tracking each column separately, or forgetting to wrap beyond Z using modulo arithmetic.



Final Answer:
mve


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