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Dictionary Order & Alphabet

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medium importance~1-2 Q in Tier 13 formulas⚡ 4 shortcuts4 subtopics
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Subtopic 3 of 4·← Arranging words and picking slots·Dictionary rank and word surgery →

Letter positions and shifts

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Memorise the anchor word EJOTY: E=5, J=10, O=15, T=20, Y=25. Every position question becomes a small shift:

  • Letter at position p: read off from EJOTY, adjust by the difference.
  • p-th from the right: position = 27 − p from the left.
  • k letters to the right of position p: p + k; to the left: p − k (stay inside 1–26).

For alphabet-modification questions ('first half reversed…'), physically write the 26-letter new sequence and count — never trust mental shifting.

📖 Notes🧩 4 question types⚡ Formulas🎯 13 practice Q

Detailed notes

Positions, mirrors and letter arithmetic

These questions treat the alphabet as a numbered strip of 26 tiles and ask who stands where. Three tools cover everything.

Tool 1 — absolute positions (EJOTY). Memorise five anchors: E=5, J=10, O=15, T=20, Y=25. Every other position is a small step from an anchor: G = J − 3 = 7; R = T − 2 = 18; W = Y + 2 = 23. With anchors, "which is the 15th letter" is instant (O), and "how many letters between G and S" is 19 − 7 − 1 = 11 (subtract positions, minus one — the letters between exclude both ends).

Tool 2 — the mirror (from the right). The letter that is k-th from the right stands at position 27−k27 - k from the left (and vice versa: position p from the left is 27−p27 - p from the right). So the 9th from the right = 27−9=1827 - 9 = 18th from the left = R; and T (20th from left) is 27−20=727 - 20 = 7th from the right. The number 27 is the whole trick: 26 letters plus one.

Tool 3 — letter arithmetic. "4th to the right of the 12th from the left": convert every clause to a from-the-left position, then add or subtract on the strip. From-the-left + right-steps = add; left-steps = subtract. When a clause says "from the right", convert first (27−k27-k), then do the arithmetic:

  • 4th right of 12th from left → 12+4=1612 + 4 = 16 → P.
  • 6th left of 8th from right → 27−8=1927 - 8 = 19, then 19−6=1319 - 6 = 13 → M.

Watch the two directions: 'to the right of' adds toward Z; 'to the left of' subtracts toward A — because the strip is drawn left = A … right = Z.

Tool 4 — modified alphabets. Variants rewrite the strip first, then ask a position:

  • Full reverse: Z first … A last; position p in the reverse strip = letter 27−p27 - p of the normal strip.
  • Half reverse: first half A-M written backwards, second half normal (or Z-N backwards). Write the new 26-letter strip once, then answer by counting — never by juggling formulas.

Check every answer by touch. Confirm with anchors: position 16 must be near T (20) — 4 steps before T is P ✓. If your letter lands more than 5 away from the predicted anchor, recount; that five-second habit catches nearly every off-by-one.

Quick revision

  • EJOTY anchors: E=5, J=10, O=15, T=20, Y=25; step from them, never from A.
  • Between G and S: 19−7−1=1119-7-1=11; 'between' excludes both ends.
  • Mirror: k-th from right =27−k= 27-k from left (and the reverse).
  • Multi-clause: convert everything to from-the-left, then add (right) or subtract (left).
  • Modified strip: write it out once, then count on paper.

Off-by-one defence. Every wrong answer in this subtopic is off by exactly one step: counting the end letter in 'between', forgetting the +1 in the mirror (27, not 26), or stepping the wrong way after 'to the left of'. Anchor-verify the final letter (it must sit within 5 of the predicted anchor) and both errors disappear.

Types of questions asked

Every way this subtopic shows up in exams — how to recognise it, the formula or logic to use, and a solved example.

Type 1: Absolute position via EJOTY anchorsvery common2 practice Q
How to spot it:

'Which is the 15th letter' or 'how many letters between X and Y'.

  1. Step from the nearest anchor (E=5, J=10, O=15, T=20, Y=25).
  2. Between A and B: ∣posA−posB∣−1|posA - posB| - 1 ('between' excludes both ends).
  3. Confirm the letter sits within 5 of the predicted anchor.

Why it works: five anchors turn 26 positions into five short hops.

Example: How many letters of the alphabet are there between G and S?

posS−posG−1=19−7−1posS - posG - 1 = 19 - 7 - 1 = 11.

Type 2: Mirror positions from the rightvery common2 practice Q
How to spot it:

'k-th from the right' or 'position of letter X from the right'.

  1. From-right position = 27−27 - from-left position (and the reverse).
  2. Convert to from-left, answer with anchors, convert back if asked.
  3. Remember the 27: 26 letters + 1.

Why it works: the mirror maps the strip onto itself around the midpoint.

Example: What is the position of the letter T from the right of the alphabet?

27−2027 - 20 = 7th from the right.

Type 3: Letter arithmetic (left/right of a position)common2 practice Q
How to spot it:

'Which letter is 4th to the right of the 12th from the left' — two clauses in one question.

  1. Convert every clause to a from-the-left number (mirror any 'from the right').
  2. Right-steps add, left-steps subtract.
  3. Read the letter off the EJOTY anchors.

Why it works: the alphabet strip is a number line in disguise.

Example: Which letter is 6th to the left of the 8th letter from the right?

8th from right = 27−8=1927-8=19 (S); 19−6=1319-6=13 → M.

Type 4: Modified or reversed alphabetcommon2 practice Q
How to spot it:

'First half written in reverse', 'alphabet in reverse order', then a position question.

  1. Write the new 26-letter strip once on paper.
  2. Count the asked position on the new strip directly.
  3. For the full reverse only: reverse position p = normal letter 27−p27 - p.

Why it works: a rewrite is a one-time setup; after that it is plain counting.

Example: If the first half of the alphabet (A-M) is written in reverse order followed by N-Z, which letter is 10th from the left?

New strip: M L K J I H G F E D C B A N O ... → 10th = D.

Formulas

Position from the right
pright=27−pleftp_{\text{right}} = 27 - p_{\text{left}}

The two positions of the same letter add to 27.

Shifted position
p′=p±kp' = p \pm k

Move right (+) or left (−) by k letters, clamped to 1–26.

Shortcut tricks

⚡ EJOTY + tiny shift

Anchor at the nearest of E, J, O, T, Y and step. Position 18: T(20) − 2 = R. Two seconds, no counting.

Example: Q. Which letter is 7th to the right of the 10th letter of the alphabet?

Sol. 10th = J; 7 right → 17 = Q (J at 10, O at 15, Q at 17).

EJOTY converts every position into a ±few-step walk from an anchor.

Where students lose marks

  • Using 26 instead of 27 in from-the-right conversions.

  • Slipping past A or Z on shifts — check bounds.

  • Confusing 'letter at position 10' with '10 letters after it'.

Practice sets — 13 questions

Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.

Topic test · 13 questions

Suggested time 9 min · wrong answers go to your mistake notebook automatically.