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Coding - Decoding

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high importance~4 Q in Tier 16 formulas⚡ 10 shortcuts7 subtopics
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Subtopic 4 of 7·← Reversal and reverse-plus-shift coding·Symbol and digit coding →

Number coding

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Words are coded as numbers. The code is built from alphabet positions (A=1 ... Z=26) by one of:

  1. Position sum: CAT = 3 + 1 + 20 = 24.
  2. Sum plus/minus constant: CAT = 24 + 5 = 29.
  3. Sum times constant: CAT = 24 × 2 = 48.
  4. Position-weighted sum: CAT = 3×1 + 1×2 + 20×3 = 65.
  5. Reverse-position coding: A=26 ... Z=1 (equivalently 27 − position); CAT = 24+26+7 = 57.

Decode the rule by computing the position sum of the sample word and comparing it with the code: the offset (plus 5? times 2? weighted?) is usually visible in one step. Reverse-position coding is spotted when long letters give small codes.

📖 Notes🧩 5 question types⚡ Formulas🎯 15 practice Q

Detailed notes

What is number coding?

A word is coded as a number. You are told (or you discover) how one word turns into its number, and you must code another word the same way. Example: SUN is coded 54, so how is DOG coded?

The number is almost always built from the alphabet positions of the letters: A = 1, B = 2, ... Z = 26. The EJOTY anchors make positions fast: E = 5, J = 10, O = 15, T = 20, Y = 25.

Step 1: find the position sum of the model word

Add the positions of the model word's letters. For SUN: S = 19, U = 21, N = 14, and 19 + 21 + 14 = 54. The code 54 is exactly this sum — the rule is a plain position sum.

Step 2: compare the sum with the code

If the sum does not equal the code, look at the difference:

What you seeRule family
Code = sum of positionsplain sum (SUN = 54)
Code uses A = 26, B = 25 ... Z = 1reverse positions (27 − p)
Code = 2 × sum, sum + 10, sum − 5 ...sum with an extra step
Code grows fast for 4-letter wordsweighted sum (position × place in word)
Code = letters plus a numbermixed code (shifted letters + sum)

The question often states the rule ("sum of alphabet positions", "A = 26, B = 25..."). When it does not, this table is your test order.

The rule bank with worked examples

  1. Plain sum. SUN = 19 + 21 + 14 = 54. DOG = 4 + 15 + 7 = 26.
  2. Reverse-position sum. Treat A as 26 and Z as 1 (each letter counts 27 − its normal position). CAT = 24 + 26 + 7 = 57.
  3. Sum with an extra step. CAB: sum = 6, code 16 → the rule adds 10. Apply the same extra step to the new word.
  4. Weighted sum. Each letter's position is multiplied by its place in the word, then added. BAG = 2×1 + 1×2 + 7×3 = 25.
  5. Mixed letter-plus-number code. 'TREE' → 'USFF48': each letter moves +1 (TREE → USFF) and the position sum (48) is written after. For the new word, do both parts again from scratch.

Worked example (weighted sum)

DAB is coded 12. How is CAD coded? D×1 + A×2 + B×3 = 4 + 2 + 6 = 12 ✓. CAD = 3×1 + 1×2 + 4×3 = 3 + 2 + 12 = 17.

Common traps

  • Reusing the sample's number. In mixed codes, the number part must be recomputed for the new word — it is never copied.
  • Wrong direction. If the paper says A = 26, do not keep summing normal positions.
  • Assuming the plain sum. Always check: does the model word's plain sum equal the code? If not, find the extra step before coding the new word.
  • Adding instead of multiplying in weighted sums — B×1 + A×2 means A is multiplied by 2, not added.

Quick revision

  • Positions A = 1 ... Z = 26; EJOTY anchors give fast look-ups.
  • Test order: plain sum → reverse sum (27 − p) → sum ± r or × k → weighted (p × place) → mixed letter + number.
  • The rule must reproduce the model word's code exactly before you use it.
  • Reverse position of a letter = 27 − position. Z counts as 1, A as 26.
  • Mixed codes: shift the letters and append the fresh position sum of the new word.

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: Plain position-sum codingvery common2 practice Q
How to spot it:

A word is coded with a number close to 30-80, and the question may say 'sum of alphabet positions'.

code=∑pi\text{code} = \sum p_i
  1. Add the positions of the model word's letters (EJOTY helps).
  2. If the sum equals the code, the rule is a plain sum.
  3. Add the positions of the new word.

Why it works: the plain sum is the most common number code in SSC, Railway and Banking papers.

Example: HAT is coded 29 (sum of positions). How is PEN coded?

H + A + T = 8 + 1 + 20 = 29 ✓ (plain sum). P + E + N = 16 + 5 + 14 = 35.

Type 2: Reverse-position sum (A = 26 ... Z = 1)common2 practice Q
How to spot it:

The question says 'A = 26, B = 25 ... Z = 1', or the code is large for a short word.

code=∑(27−pi)\text{code} = \sum (27 - p_i)
  1. Convert each letter to 27 − its normal position.
  2. Add them for the model word and confirm the code.
  3. Repeat for the new word.

Why it works: reverse positions are the same table read backwards; Z = 1 and A = 26.

Example: EAT is coded 55 (A = 26, B = 25 ... Z = 1). How is TEN coded?

E = 22, A = 26, T = 7 → 55 ✓. T = 7, E = 22, N = 13 → 42.

Type 3: Position sum with an extra step (× k or + r)common2 practice Q
How to spot it:

The plain sum of the model word is close to, but not equal to, the code.

code=k∑pi+r\text{code} = k\sum p_i + r
  1. Compute the plain sum of the model word.
  2. Find the extra step: code − sum, or code ÷ sum.
  3. Apply the same step to the new word's sum.

Why it works: a single extra operation turns the plain sum into any number the setter wants.

Example: DIG is coded 22. How is BIG coded?

D + I + G = 4 + 9 + 7 = 20; 20 + 2 = 22, so the rule is sum + 2. BIG = 2 + 9 + 7 = 18, plus 2 = 20.

Type 4: Weighted sum (position × place in the word)occasional2 practice Q
How to spot it:

The code cannot be reached by any plain sum; the word has 3-4 letters and the code is mid-sized.

code=∑i⋅pi\text{code} = \sum i \cdot p_i
  1. Multiply each letter's position by its place (1st, 2nd, 3rd ...).
  2. Add the products and check the model word's code.
  3. Do the same for the new word.

Why it works: weighting explains codes that no flat sum can reach.

Example: DAB is coded 12 (position × place). How is CAD coded?

D×1 + A×2 + B×3 = 4 + 2 + 6 = 12 ✓. CAD = 3×1 + 1×2 + 4×3 = 3 + 2 + 12 = 17.

Type 5: Mixed letter-plus-number codeoccasional2 practice Q
How to spot it:

The code is a string like 'USFF48' — letters followed by a number (or the reverse).

  1. Solve the letter part first (usually a shift).
  2. Compute the number part for the NEW word afresh (usually its position sum).
  3. Join both parts in the same order as the sample.

Why it works: the two halves are independent mini-codes; the number always changes with the word.

Example: TREE is written USFF48 (+1 letters, position sum appended). How is LEAF written?

LEAF + 1 = MFBG. Sum = 12 + 5 + 1 + 6 = 24. Code = MFBG24.

Formulas

Position sum
code=∑Q(wi)\text{code} = \sum Q(w_i)

Q = A1..Z26 positions.

Affine code
code=k⋅∑Q(wi)+r\text{code} = k \cdot \sum Q(w_i) + r

Fit k and r from the sample pair.

Weighted sum
code=∑i⋅Q(wi)\text{code} = \sum i \cdot Q(w_i)

Letter i multiplies its position.

Reverse positions
Qrev(c)=27−Q(c)Q^{rev}(c) = 27 - Q(c)

Z=1 ... A=26; small codes for long words.

Shortcut tricks

⚡ One sample fixes the affine code

Compute the position sum S of the sample. If code = S → plain sum. If code − S is constant-looking (5, 10...) the rule is S + r. If code/S is a clean 2 or 3, the rule is k·S. If neither fits, try the weighted sum.

Example: Q. If SUN = 54 (19+21+14), code MOON.

Sol. Code = plain position sum. M+O+O+N = 13+15+15+14 = 57.

Position sum first — it explains over half of CGL number codes.

⚡ Digit-sum shortcut for 9-heavy checks

Position sums reduce nicely: letters at EJOTY anchors contribute 5/10/15/20/25. Sums are easy to verify by grouping anchors instead of adding letter by letter.

Example: Q. In position-sum coding, is CAT coded as 24?

Sol. C = 3, A = 1 and T = Y − 5 = 25 − 5 = 20. Total = 3 + 1 + 20 = 24 ✓.

Anchors (E=5, J=10, O=15, T=20, Y=25) turn position look-ups into small ± adjustments.

Where students lose marks

  • Using A=0 indexing by mistake — CGL always uses A=1 unless a sample proves otherwise.

  • Adding the constant to each letter instead of to the total (S + r per letter vs once).

  • Ignoring the weighted variant when the plain sum is off by a non-constant amount.

Practice sets — 15 questions

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

Topic test · 10 questions

Suggested time 7 min · wrong answers go to your mistake notebook automatically.