Alphabet coding pattern – complete the next three-letter group: ejo tyd ins xch ?

Introduction / Context:
This is a letter-coding sequence where each three-letter block follows a fixed internal rule, and successive blocks shift by a constant offset through the alphabet. Recognizing the numeric positions of letters and modular wrap-around (after Z comes A) is essential.

Given Data / Assumptions:

• Blocks: ejo, tyd, ins, xch, ?
• Use A=1, B=2, …, Z=26. Alphabet wraps around at 26.
• Exactly one correct three-letter answer continues the established rule.

Concept / Approach:
First, analyze any single block. In “ejo”, positions are e=5, j=10, o=15. Each successive letter is +5 from the previous. Check the other blocks for the same pattern and then determine how the first letter of each block moves from block to block.

Step-by-Step Solution:
Inside each block: apply +5 repeatedly: start → start+5 → start+10.Block 1 “ejo”: 5 → 10 → 15 (valid).Block 2 “tyd”: t=20 → y=25 → d=4 (since 25+5=30, wrap to 4).Block 3 “ins”: i=9 → n=14 → s=19 (valid).Block 4 “xch”: x=24 → c=3 → h=8 (valid).Now track the starting letters: e(5) → t(20) → i(9) → x(24). Each jump is +15 with wrap (5+15=20; 20+15=35→9; 9+15=24).Next start = 24+15=39→13 = m. Then apply +5 twice: m(13) → r(18) → w(23).

Verification / Alternative check:
Confirm both rules simultaneously: inter-block start shift of +15 with wrap, and intra-block step of +5 twice. “mrw” satisfies both, so it is the unique continuation.

Why Other Options Are Wrong:

• nrw and nsx use the correct last two letters but the starting letter violates the +15 start-step.
• msx changes the internal +5 +5 pattern.

Common Pitfalls:

• Forgetting wrap-around arithmetic (mod 26), which is why letters like y→d or x→c appear.
• Matching only one of the two rules (start shift or internal step) but not both.

Final Answer:
mrw