Analytical Reasoning & Intelligence Tests — Chapter 3

Coding-Decoding

Why this chapter matters: Coding-decoding is the smallest reasoning family in Subject 12, and the cheapest marks in it: every item gives you its own rule in the stem, so nothing has to be memorised — you only have to read the given pair correctly and apply it without changing it halfway. The script count behind this chapter (Section 10) finds 11 genuine coding-decoding stems across 9 distinct source files, from FPSC 2015 and 2017 papers through a PPSC 2020 paper to CSS GSA 2024 and CSS MPT 2026 recall. Eleven stems is a thin bank, and this chapter is honest about that: it teaches the four code types those stems actually use, works every genuine stem, and flags the two printed quirks in the bank rather than smoothing them over. If you can do these eleven, you can do any coding item the papers set, because no new type appears outside them.

Status of this chapter (read first): this is AR-03, written 31 October 2026 in taxonomy order after AR-02. The Subject 12 structure page claimed no mark for this family at structure level because its paper-level spread had not been verified file by file; that verification is done in this run (Section 10), and the marks in the Exam Trend box below rest on it — not on the structure page’s counts alone.

Exam Trend box

• 🔁 Most Repeated: Coding-decoding as a family — 11 genuine stems across 9 distinct source files, clearing the 🔁 paper-count limb (≥5 different papers). The exam-paper sources alone are six: FPSC Assistant Director Welfare Department 2015 (×2 stems), FPSC Assistant Director Ministry of Defence 2017, PPSC Junior Clerk BS-11 Anti-Corruption Establishment 2020, NTS Assistant Director LDA, CSS GSA 2024, and CSS MPT 2026 paper recall — plus three CSS MPT General Abilities practice-set files.
• ⭐ Must Know: Letter-shift, letter-number value and reversal codes — 🔁 and still asked in 2024 and 2026 papers: CSS GSA 2024 supplies the +1 shift stem (CHAIR → DIBJS), and CSS MPT 2026 recall supplies the letter-value sum stem (DOG = 26 → BAT = 23). Expect one coding item in a reasoning section, usually a shift or a value sum.
• 🆕 Newly Appeared / Recent Trend: none claimed. Coding items run continuously from FPSC 2015 to CSS MPT 2026; their 2025–26 signal is continued presence in the CSS MPT General Abilities section, not first appearance.

1. The method — five steps, in order

1. Write the given pair letter by letter. Put the plain word above its code, position by position. Never work from the whole word at a glance — every coding error in the banks comes from reading a word, not a letter.
2. Name the operation. For each position, ask: shift by a fixed number? Reversed order? Replaced by its alphabet number? Replaced by a fixed substitute letter? The operation must be the same at every position, or you have not found it yet.
3. Test it on every letter of the given pair. A rule that works for three letters and fails the fourth is not the rule — go back to step 2. (The one exception is a printed misprint, Section 6 — and even there, the stem’s own answer and explanation settle it.)
4. Apply it, unchanged, to the asked word. Do not “improve” the rule halfway through the word.
5. Wrap around. After Z comes A (and before A comes Z). A +1 shift sends Y to Z and Z to A; a −1 shift sends A to Z.

Write A = 1 … Z = 26 in the margin before you start. Half of this chapter’s items are value items, and every one of them is a margin-strip question.

2. Core notes — the four code types the banks actually use

2.1 Letter-shift codes (fixed shift, same at every letter)

• Rule: each letter moves the same number of places forward (or back) in the alphabet. Find the shift from the first letter, then confirm it at every other letter.
• Worked example (banked): “If each letter is shifted by +1 (A→B, B→C, …), then CHAIR becomes:” — C→D, H→I, A→B, I→J, R→S, so DIBJS (CSS GSA 2024, maths Q31–60). The stem hands you the shift; the work is only applying it five times.
• Worked example (banked): “If STRAY is coded as TUSBZ then how will MOURN be coded?” — S→T, T→U, R→S, A→B, Y→Z: +1 at every position. So M→N, O→P, U→V, R→S, N→O = NPVSO (FPSC Assistant Director, Welfare Department, 2015). Note Y→Z: the shift does not wrap here, but it would if a letter were Z.
• Worked example (banked, with a misprint — see Section 6): the NTS Assistant Director LDA paper prints the same item with the code as “TISBZ”, but its own answer is NPVSO and its own explanation states the +1 rule letter by letter (M→N, O→P, U→V, R→S, N→O). The answer follows the rule, not the misprinted second letter — follow the rule.

2.2 Letter-number value codes (A = 1 … Z = 26)

Two different questions hide under this one heading, and confusing them is the chapter’s main trap (Section 6):

• (a) Value-sum codes: add the letters’ positions.
• Worked example (banked): “If DOG = 26, then BAT = ?” — D(4) + O(15) + G(7) = 26, so B(2) + A(1) + T(20) = 23 (CSS MPT 2026 paper recall). The given pair exists only to prove the rule is “add”, not “concatenate”.
• Worked example (banked): “If Z = 26 and NET = 39, then NUT = ?” — N(14) + E(5) + T(20) = 39, so N(14) + U(21) + T(20) = 55 (CSS MPT maths booklet remainder practice set). The Z = 26 anchor confirms the A = 1 numbering; without it, a solver might try A = 0.
• (b) Single-letter value: the asked item is one letter.
• Worked example (banked): “If A = 1, Z = 26, then J = ?” — count A(1), B(2), C(3), D(4), E(5), F(6), G(7), H(8), I(9), J(10) (CSS MPT General Abilities practice set). Trivial once the strip is written; the trap is counting from A = 0.
• (c) Value-concatenation codes: write the positions side by side instead of adding them.
• Worked example (banked): “If A = 1, B = 2, C = 3, then ‘BAD’ = ?” — B(2), A(1), D(4) written in order = 214 (CSS MPT 2026 full mock test). If you added, you would answer 7 — and 7 is not among the options. The given trio A = 1, B = 2, C = 3 tells you the numbering; the answer’s three-digit shape tells you the operation is concatenation, not addition. Compare Section 2.2(a): same numbering, opposite operation — the stem and the options together decide which.

2.3 Substitution codes (a fixed letter-for-letter map)

• Rule: the given pair defines a map — each plain letter is replaced by one fixed code letter, with no uniform shift. Build the map from the pair, then read the asked word through it. Letters not in the given pair cannot be coded this way, so the asked word in a fair item uses only mapped letters.
• Worked example (banked): “If STOVE is written as FNBLK, how is VOTES written in that code?” — map: S→F, T→N, O→B, V→L, E→K. This is not a shift (S→F is −13, T→N is −6), so shift-hunting fails here. Read VOTES through the map: V→L, O→B, T→N, E→K, S→F = LBNKF (FPSC Assistant Director, Ministry of Defence, 2017). Note VOTES is an anagram of STOVE — every letter is already in the map, which is what makes the item solvable.
• Worked example (banked): “If MONDAY = 123456, then DAY = ?” — map: M→1, O→2, N→3, D→4, A→5, Y→6. Read DAY through it: D→4, A→5, Y→6 = 456 (CSS MPT General Abilities practice set). Same skill as STOVE, with digits instead of letters — a substitution map, not arithmetic.

2.4 Reversal codes (reverse the order, then optionally shift)

• Rule: reverse the word first. If the reversed word does not match the given code, apply one uniform shift to the reversed word and test again.
• Worked example (banked): “PEACH is to HCAEP then 26541 should be?” — PEACH reversed is HCAEP, a pure reversal with no shift. Reverse the digits the same way: 26541 reversed = 14562 (PPSC Junior Clerk BS-11, Anti-Corruption Establishment, Punjab, 2020). The item changes alphabets (letters → digits) but not operations.
• Worked example (banked): “In a certain code ‘DESCRIBE’ is written as ‘Fcj sdtfe’. How will ‘CONSIDER’ be written in that code?” — first reverse DESCRIBE: EBIRCSED. Then +1 each letter: F, C, J, S, D, T, F, E = FCJSDTFE, which is the printed code ignoring its stray space and mixed case (“Fcj sdtfe”). Apply the same two steps to CONSIDER: reverse → REDISNOC, +1 each → S, F, E, J, T, O, P, D = SFEJTOPD (FPSC Assistant Director, Welfare Department, 2015). The stem’s printed code looks garbled until you reverse first — that is the whole difficulty of the item, and the reason step 1 of Section 1 says to write the pair letter by letter.

3. Master table — code type → test → bank example

4. Rapid-fire one-liners

• Pair first, rule second: write the given pair letter by letter before naming any operation.
• One rule, every letter: a shift that works for three letters and fails the fourth is not the rule.
• A = 1 strip in the margin, every time — value items are won there, not in your head.
• Sum or string? DOG = 26 proves “add”; BAD = 214 proves “concatenate”. The given pair and the options’ shape decide.
• Substitution is not shift: if the shifts differ letter to letter (STOVE → FNBLK), stop shifting and build the map.
• Reverse before you shift: DESCRIBE only yields its code after reversal.
• After Z comes A; before A comes Z. Check the wrap on every shift item, even when this item does not need it.

5. Most-asked facts

• 🔁 Letter-shift (+1) and letter-value sum are the two shapes that recur across bodies and years: FPSC 2015 (shift), FPSC 2017 (substitution), PPSC 2020 (reversal), CSS GSA 2024 (shift), CSS MPT 2026 recall (value sum). A reasoning section that sets one coding item will almost certainly set one of these two.
• ⭐ The +1 shift is the single most portable rule in the family: it appears in the CSS GSA 2024 paper, the FPSC 2015 paper and the NTS paper, each time with the same answer shape (NPVSO for MOURN in both the FPSC and NTS versions).
• The substitution and reversal items are one-offs each in this bank, but they are the items that separate full marks from partial marks — they are solved by method (Section 1), not by memorising more codes.

6. Traps & confusions

• Sum vs concatenation (the BAD trap). A = 1, B = 2, C = 3 with BAD gives 214 (positions in order), not 7 (their sum). If the answer options are multi-digit strings, the operation is concatenation; if the given pair is a single number equal to a sum (DOG = 26), the operation is addition. Read the given pair, not your habit.
• Shift vs substitution (the STOVE trap). STOVE → FNBLK has different shifts at different letters (−13, −6, …), so it is not a shift code at all — it is a map. Hunting for a shift that is not there wastes the item; building the map answers it in seconds.
• The NTS misprint (read the answer, not just the code). The NTS LDA paper prints “STRAY is coded as TISBZ”, whose second letter breaks the +1 rule — but the same stem’s answer is NPVSO and its own explanation walks the +1 rule letter by letter (M→N, O→P, U→V, R→S, N→O). The printed TISBZ is a misprint; the FPSC 2015 twin stem prints the same item correctly as TUSBZ. Teach the rule, flag the misprint, do not invent a rule that produces TISBZ.
• The DESCRIBE printing quirk. The FPSC 2015 stem prints the code as “Fcj sdtfe” — mixed case with a stray space. Ignoring case and the space, its letters are FCJSDTFE, exactly the reverse-then-+1 of DESCRIBE. Do not let typesetting hide a clean rule.
• “Encoding” is not coding-decoding. The topic rule that counts this chapter also catches one computer-science stem (“When a key is pressed on the keyboard, which standard is used for converting the keystrokes into the corresponding bits?” — answer ASCII, PPSC Assistant Director Research, 2025) because its topic is “Encoding”. That is a CS fact (CS chapters carry ASCII), not a reasoning code, and it is counted in the scan total but excluded from this chapter’s teaching and from the 11 genuine stems. The practice query in the front-matter excludes the “Encoding” tag for the same reason.
• No code-language sentences in this bank. Standard reasoning books also teach sentence codes (“apple is red” = ”…”), but no bank stem in scope uses that type. It is not taught here, and it is not smuggled in as a worked example from outside the banks.

7. Memory tricks

• “Shift–Value–Map–Reverse”: the four families of Section 2, in the order to test them. Say the four words when you meet a coding item; the given pair will point to one of them within two letters.
• Alphabet strip, twice: write A = 1 … Z = 26 once for value items and once, reversed, for shift items that wrap past Z.
• “Pair, rule, test, apply”: the four verbs of Section 1. If you skipped the test step, you have not solved the item yet.
• MOURN = NPVSO as the anchor example: one +1 shift, five letters, no wrap — if a new item feels harder than this, you have probably misread the given pair; re-write it.

8. Visuals (specs only — site build renders these)

• Worked-example panels: each Section 2 example with the plain word above its code, arrows showing the per-letter operation (shift arrows, position numbers, map lines, reversal arrow).
• Reference card: the A = 1 … Z = 26 strip, placed before Section 2, plus a Z→A wrap reminder.
• Decision tree: the four families of Section 2 as a flowchart (uniform shift? → value? → map? → reversal?) placed after Section 1.

9. Practice this topic

Pull a timed set from the verified banks using the practice query in the front-matter (topic tags Coding / Coding-decoding / Letter coding): 11 genuine stems across 9 distinct files. Book mode: ← Previous: Number & Letter Series, Sequences & Odd One Out (AR-02) · Next: Direction Sense (AR-04) →

Sources & count (Section 10 honesty note). Count by script hidden_files/goldmine-notes-count-ar03.py (counts JSON hidden_files/goldmine-notes-ar03-counts.json), same bank dirs and topic-based classification order as the Subject 12 structure count (hidden_files/goldmine-notes-count-ar12.py): 583 files / 56,388 questions scanned; 12 rows including duplicates; 12 unique topic rows across 10 distinct files; filename-year files 2024: 1, 2025: 1, 2026: 2. Of those 12 rows, 11 are genuine coding-decoding stems across 9 distinct files and 1 is a false positive: the PPSC Assistant Director Research 2025 “Encoding” stem, whose topic contains “coding” but whose content is the computer-science ASCII fact (answer ASCII) — excluded from teaching, from the 11, and from the practice query. Genuine-stem sources: CSS GSA 2024 maths Q31–60 (1), CSS MPT 2026 full mock test (1), CSS MPT 2026 paper recall (1), CSS MPT General Abilities practice set (2), CSS MPT maths booklet remainder practice set (1), FPSC Assistant Director Ministry of Defence 2017 (1), FPSC Assistant Director Welfare Department 2015 (2), NTS Assistant Director LDA (1), PPSC Junior Clerk BS-11 Anti-Corruption Establishment 2020 (1). Classification is topic-based only, so untagged coding items inside general papers are not counted: 11 is a floor, stated honestly, not an estimate. Every banked answer taught here was verified by hand against its stem in this run: the STOVE substitution, the DESCRIBE reverse-then-+1, and the PEACH digit reversal were each recomputed letter by letter; the NTS TISBZ misprint is flagged in Section 6 from the stem’s own explanation, not silently corrected. No fact in this chapter comes from memory; methods are standard procedural types, and every worked example is a bank stem with its banked answer.