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A→E +4 Σ 26 ↺
Reasoning · Chapter 4

Coding and Decoding

Two to three marks every shift, and AAI reuses the same four mechanisms year after year. Six of the questions in this chapter are lifted straight from the real papers.

Concept video — watch on the AAI ATC Exam Prep channel
2–3questions per shift
45 sectarget time each
5code types
6verified PYQs inside
Objectives 1. Letter shifts 2. Reverse coding 3. Number-sum codes 4. Message coding 5. Letter clusters Summary Assessment Free PDF
Before you start

Learning objectives and outcomes

This whole chapter rests on one thing: knowing the position number of every letter without counting. Everything after that is arithmetic.

Objective 1Recall the position of any letter instantly using the EJOTY anchors, forwards and backwards.
Objective 2Detect a uniform shift by testing the first letter pair, then confirm on the last.
Objective 3Recognise reverse-then-shift codes, where the word is flipped before the arithmetic.
Objective 4Solve number codes built on the sum of letter positions, including the constant-offset variety AAI favours.
Outcome ACrack a letter code in under 45 seconds without writing the full alphabet.
Outcome BSolve message-substitution questions by intersecting the given sentences.
Subtopic 1

Letter position and uniform shifts

Nothing in this chapter works until letter positions are automatic. Counting from A every time costs you the question. Use the five anchors instead.

The EJOTY anchors

E = 5  ·  J = 10  ·  O = 15  ·  T = 20  ·  Y = 25

Any letter is now at most two steps from an anchor. R is two after O, so R = 17. W is two after T, so W = 22. For the reverse position, subtract from 27: the reverse of R is 27 − 18 = 9.

A1 B2 C3 D4 E5 F6 G7 H8 I9 J10 K11 L12 M13
N14 O15 P16 Q17 R18 S19 T20 U21 V22 W23 X24 Y25 Z26

A uniform shift adds the same number to every letter, wrapping around from Z back to A. Test the first letter pair to find the shift, then confirm with the last. If both agree, apply it to the answer word without checking the middle.

Figure 4.1 — The alphabet wheel A circular alphabet with an arrow showing a +4 shift and the wrap-around from Y and Z back to C and D. Upload image here
✈ AAI ATC relevance — letter-shift coding appeared in both 2025 shifts and in the 2021 papers
Memory trick — "First and last, then go"

Never verify all seven letters. Check letter one, check the final letter, and if the shift matches, trust it. That habit alone saves twenty seconds per question.

Worked example — 2025 Shift 1 paper

PARENTS is related to TEVIRXW, and ACHIEVE is related to EGLMIZI. To which option is PROUDLY related?

  1. P = 16, T = 20. The shift is +4.
  2. Confirm on the last letter: S = 19, W = 23. Also +4. The rule holds.
  3. Apply to PROUDLY: P→T, R→V, O→S, U→Y, D→H, L→P.
  4. Y = 25, and 25 + 4 = 29. Subtract 26 to wrap: 3 = C.
  5. Answer: TVSYHPC. The wrap on the final Y is the entire difficulty of this question.
EasyATC Pattern
If CAT is coded as FDW, how is DOG coded in the same language?
C = 3 and F = 6, so the shift is +3. Confirm on the last letter: T = 20 and W = 23, also +3. Applying +3 to DOG gives D→G, O→R, G→J, so the code is GRJ.
ModeratePYQ 2025 · Shift 1
PARENTS is related to TEVIRXW based on English alphabetical order. In the same way, ACHIEVE is related to EGLMIZI. To which option is PROUDLY related?
The shift is +4 throughout, confirmed on both given words. PROUDLY becomes T, V, S, Y, H, P and then Y + 4 wraps past Z to C — giving TVSYHPC. Three of the four options are built by getting one letter of the wrap or one middle letter wrong.
HardATC Pattern
If FLIGHT is coded as UORTSG, what is the code for RUNWAY?
This is not a shift — it is the opposite-letter rule, where each letter maps to 27 minus its position. F = 6 goes to 21 = U, L = 12 goes to 15 = O, and so on. For RUNWAY: R = 18 → 9 = I, U = 21 → 6 = F, N = 14 → 13 = M, W = 23 → 4 = D, A = 1 → 26 = Z, Y = 25 → 2 = B. The code is IFMDZB.
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Subtopic 2

Reverse coding and varying shifts

When a uniform shift refuses to fit, two things are usually going on: the word has been reversed before coding, or the shift changes position by position. The 2021 Shift 2 paper used both at once.

How to spot it

If the first letters do not fit a shift, immediately test the first code letter against the last original letter. If that fits, the word is reversed. Then read the shifts across the reversed word — they often descend 5, 4, 3, 2, 1 or ascend 1, 2, 3.

Reverse the word first  →  then apply the shift pattern  →  read off the code
Figure 4.2 — Reverse-then-shift decoded The word ABOUT written forwards and reversed underneath, with the descending shifts +5 +4 +3 +2 +1 drawn as arrows onto YYRDB. Upload image here
Memory trick — "Shift fails? Flip it."

The moment a straight shift does not work on letter one, write the word backwards. Two-thirds of the time the pattern appears immediately.

Worked example — 2021 Shift 2 paper

ABOUT is written as YYRDB, and ACUTE is written as JXXEB. How is ANGLE written?

  1. A → Y as a straight shift makes no sense, so reverse ABOUT to get TUOBA.
  2. T = 20 → Y = 25 is +5. U = 21 → Y = 25 is +4. O = 15 → R = 18 is +3. B = 2 → D = 4 is +2. A = 1 → B = 2 is +1.
  3. The pattern is reverse the word, then add 5, 4, 3, 2, 1.
  4. Confirm on ACUTE: reversed is ETUCA, giving E+5 = J, T+4 = X, U+3 = X, C+2 = E, A+1 = B — exactly JXXEB.
  5. ANGLE reversed is ELGNA: E+5 = J, L+4 = P, G+3 = J, N+2 = P, A+1 = B. Answer: JPJPB.
EasyATC Pattern
If TIME is coded as EMIT, what is the coding rule?
Reading TIME backwards gives EMIT exactly, with no arithmetic at all. Whenever the code word contains the same letters as the original, check reversal before anything else.
ModeratePYQ 2021 · Shift 2
In a certain code language, ABOUT is written as YYRDB, and ACUTE is written as JXXEB. How will ANGLE be written in that language?
Reverse the word, then add 5, 4, 3, 2, 1 across the five letters. ANGLE reversed is ELGNA, which becomes J, P, J, P, B. Notice how closely the wrong options resemble the right one — this is why the last letter must be checked, not assumed.
HardATC Pattern
If TOWER is coded as SPVFQ, what is the code for RADAR?
The shifts alternate minus one, plus one across the five positions: T→S, O→P, W→V, E→F, R→Q. Applying the same pattern to RADAR gives R−1 = Q, A+1 = B, D−1 = C, A+1 = B, R−1 = Q, so the code is QBCBQ. Option 4 changes only the middle letter, which is where a careless reader lands.
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Subtopic 3 · highest yield

Number codes from letter sums

This is the format AAI has used in both 2025 shifts. A word is given a two-digit number, and you have to find the arithmetic. Nine times out of ten it is built on the sum of the letter positions.

The three sums worth testing, in order

1. Plain sum of letter positions
2. Sum plus or minus a constant
3. Sum divided by the number of letters

Compute the plain sum for the first given word and compare it with its code. The gap is your constant. Then verify that same gap on the second word. If it matches, apply it.

Figure 4.3 — Sum-plus-constant method A worked grid showing LOUNGE broken into 12, 15, 21, 14, 7, 5, totalled to 74, with +6 arrowed across to 80. Upload image here
Memory trick — "Sum it, then mind the gap"

Add the letter positions first, always. The difference between your sum and the given code is the constant, and AAI has used +6 in both 2025 shifts.

Worked example — 2025 Shift 1 paper

LOUNGE is coded as 80 and PARCEL is coded as 61. What is the code for ZEALOT?

  1. LOUNGE = 12 + 15 + 21 + 14 + 7 + 5 = 74. The code is 80, so the gap is +6.
  2. Check on PARCEL = 16 + 1 + 18 + 3 + 5 + 12 = 55. The code is 61, again a gap of +6. Rule confirmed.
  3. ZEALOT = 26 + 5 + 1 + 12 + 15 + 20 = 79.
  4. 79 + 6 = 85.
ModeratePYQ 2025 · Shift 1
In a certain code language, LOUNGE is coded as 80 and PARCEL is coded as 61. What is the code for ZEALOT?
Both given words follow sum of letter positions plus six. ZEALOT sums to 79, and 79 + 6 = 85. Option 4 is the trap for anyone who forgets to add the constant.
ModeratePYQ 2025 · Shift 2
In a certain code language, MATTER is coded as 83 and SOLIDS is coded as 84. What is the code for LIQUID?
MATTER sums to 77 and SOLIDS to 78, each six less than its code — the same plus-six rule as Shift 1. LIQUID = 12 + 9 + 17 + 21 + 9 + 4 = 72, so the code is 78. Option 3 is the plain sum, left in deliberately.
HardATC Pattern
If SIGNAL is coded as 57 and RADAR is coded as 37, what is the code for TOWER?
SIGNAL sums to 19 + 9 + 7 + 14 + 1 + 12 = 62, and the code is 57 — five less, not more. Check on RADAR: 18 + 1 + 4 + 1 + 18 = 42, and the code is 37, again five less. TOWER sums to 20 + 15 + 23 + 5 + 18 = 81, so the code is 76. Option 2 is the plain sum, planted for anyone who assumes the constant is always added.
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Subtopic 4

Message and substitution coding

Here whole words are replaced by nonsense words. You are given two or three coded sentences and asked for the code of one word. The method is pure intersection — no alphabet, no arithmetic.

The intersection method

  1. Find the word that appears in two English sentences.
  2. Find the code word that appears in the matching two coded sentences.
  3. Those two must correspond. Lock the pair.
  4. Cancel that pair out and repeat with what is left.
Figure 4.4 — Intersecting two coded sentences Two sentence pairs written one above the other with the shared word and shared code circled and joined by an arrow. Upload image here
Memory trick — "Shared word, shared code"

If a word appears in two sentences and one code word appears in the same two sentences, they are the same thing. No other reasoning is needed.

Worked example — 2021 Shift 3 paper

'Tudo Bem' is written as 'All Fine', 'Como Esta' is written as 'How You', and 'Bem Como' is written as 'Fine You'. How is 'Tudo Esta' written?

  1. Bem appears in sentences 1 and 3. The English word appearing in both is Fine. So Bem = Fine.
  2. Sentence 1 is 'Tudo Bem' = 'All Fine'. Removing Bem and Fine leaves Tudo = All.
  3. Como appears in sentences 2 and 3. Removing Bem from sentence 3 leaves Como = You.
  4. Sentence 2 is 'Como Esta' = 'How You'. Removing Como and You leaves Esta = How.
  5. 'Tudo Esta' therefore reads All How.
EasyPYQ 2025 · Shift 2
In a certain code language, 'creativity sparks innovation' is coded as 'tk jo lo' and 'innovation is needed' is coded as 'mb pt jo'. How is 'innovation' coded?
The only English word appearing in both sentences is innovation, and the only code word appearing in both is jo. They must be the same word. This is the easiest mark in the entire reasoning section — never skip it.
ModeratePYQ 2021 · Shift 3
'Tudo Bem' is written as 'All Fine', 'Como Esta' is written as 'How You', and 'Bem Como' is written as 'Fine You'. How will 'Tudo Esta' be written in the same language?
Bem = Fine and Como = You come straight from the overlaps, which then forces Tudo = All and Esta = How. So 'Tudo Esta' is 'All How'. Note that word order in the answer follows the order given in the question.
HardATC Pattern
'ka pi ro' means 'tower controls flight', 'ro zi ba' means 'flight is delayed', and 'pi zi na' means 'controls is manual'. What is the code for 'tower'?
Flight appears in sentences 1 and 2, and ro appears in both, so ro = flight. Controls appears in 1 and 3, and pi appears in both, so pi = controls. Sentence 1 has three words, and with ro and pi assigned, the only code left is ka, which must mean tower.
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Subtopic 5

Letter clusters and mixed codes

AAI is fond of three-letter clusters like FPJ, BLF, JTM, MWQ, where you must find the internal gap pattern. The 2025 papers carried several, sometimes as odd-one-out and sometimes as analogy.

Read the gaps, not the letters

Convert the cluster to numbers, then write the differences between consecutive letters. Three of the four clusters will share the same difference pattern; the fourth is your answer, or the pattern carries over to a new cluster.

FPJ → 6, 16, 10 → gaps +10, −6
BLF → 2, 12, 6 → gaps +10, −6
Figure 4.5 — Cluster gap analysis Four clusters written as number triples with the gaps drawn beneath each, and the odd one circled. Upload image here
Memory trick — "Numbers first, always"

Never stare at letter clusters as letters. Convert all four to numbers in one pass, then compare gaps. The odd one becomes obvious in five seconds.

EasyATC Pattern
Which cluster does not belong: FPJ, BLF, JTM, MWQ?
FPJ is 6, 16, 10 with gaps of +10 then −6. BLF is 2, 12, 6 with the same gaps. MWQ is 13, 23, 17, again +10 then −6. JTM is 10, 20, 13, which gives +10 then −7. JTM is the odd one out.
ModerateATC Pattern
If ACE is related to BDF, then GIK is related to:
Each letter moves forward by one: A→B, C→D, E→F. Applying the same to GIK gives G→H, I→J, K→L, so the answer is HJL. The internal gap of two inside the cluster is preserved, which is what the other options break.
HardATC Pattern
In the sequence AFH, DJK, GNN, JRQ, what comes next?
Take each position separately. The first letters run A, D, G, J — a step of +3, so next is M. The second letters run F, J, N, R — a step of +4, so next is V. The third letters run H, K, N, Q — a step of +3, so next is T. The answer is MVT. Reading columns rather than whole clusters is the entire technique.
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Exam strategy

Six tips that hold in the AAI ATC hall

Write EJOTY in the marginFirst thing, before you read the question. It pays for itself twice over.
Test first and last onlyIf both letters agree on the shift, apply it. Checking the middle wastes time.
Number codes mean sumsAdd the letter positions before trying anything cleverer.
Watch the wrapY and Z with a positive shift are where the wrong option is planted.
Message codes are free marksPure intersection, no arithmetic. Never leave one unattempted.
Clusters go column by columnCompare first letters together, then second, then third.
Quick revision

Chapter summary sheet

EJOTYE5 · J10 · O15 · T20 · Y25 — every letter is within two of an anchor.
Reverse position27 minus the forward position.
Uniform shiftSame number added to every letter, wrapping Z back to A.
Opposite lettersA↔Z, B↔Y, C↔X. Position becomes 27 minus itself.
Reverse-then-shiftFlip the word first, then apply a descending or ascending shift.
Number codesSum of letter positions, usually plus a constant. AAI used +6 in both 2025 shifts.
Message codesShared English word plus shared code word equals a locked pair.
ClustersConvert to numbers, compare gaps, or read column by column.
Time budget45 seconds. If the pattern has not appeared in two attempts, move on.

↓ Free download — Coding and Decoding question PDF

Four pages of practice covering all five code types, with a blank alphabet-position grid and working space left for your letter arithmetic. Print it, solve it, keep it.

End of chapter

Comprehensive assessment

Nine question formats, building in difficulty. Full solutions are in the downloadable PDF above.

A · Multiple choice questions

1. If BOOK is coded as CPPL, what is the code for PAGE?
2. If SUN is coded as HFM using opposite letters, what is the code for MOON?
3. If a word codes to the sum of its letter positions plus 6, what does CAB code to?
4. Which cluster does not belong: DGJ, HKN, MPS, QTX?
5. If 'mo ta' means 'blue sky' and 'ta re' means 'sky high', what does 'ta' mean?

B · Assertion and reason

6. Assertion: The reverse position of a letter equals 27 minus its forward position. Reason: The alphabet has 26 letters, so positions pair symmetrically around the centre.
7. Assertion: Verifying the first and last letters is enough to confirm a uniform shift. Reason: A uniform shift applies the same increment to every letter.

C · Match the following

Column I — code typeColumn II — method
(a) LOUNGE = 80(i) Reverse then shift 5, 4, 3, 2, 1
(b) ABOUT = YYRDB(ii) Intersection of shared words
(c) 'Bem Como' = 'Fine You'(iii) Sum of letter positions plus a constant
(d) PARENTS = TEVIRXW(iv) Uniform shift of +4

D · Fill in the blanks

8. The EJOTY anchors are E = 5, J = 10, O = , T = 20 and Y = .
9. The opposite letter of D is .
10. In both 2025 shifts, the constant added to the letter-position sum was .
11. When a straight shift fails on the first letter, the next thing to try is .

E · True or false

12. A uniform shift wraps from Z back to A.
13. Message-substitution questions require letter arithmetic.
14. ZEALOT sums to 79 before any constant is added.
15. Letter clusters should be compared as whole words rather than column by column.

F · Short answer

16. Write the EJOTY anchors and explain how to find the position of W in under three seconds.
17. Describe the intersection method for message coding in three steps.
18. Why is the wrap-around at Y and Z the most common source of error in shift codes?

G · Long answer

19. Explain the full method for number codes built on letter sums, then apply it to a word of your choice, showing every step.
20. Take ABOUT = YYRDB and ACUTE = JXXEB. Derive the rule from scratch, prove it on both words, and apply it to a fresh five-letter word.

H · HOTS — higher order thinking

21. Two different coding rules both produce the same code for a given word. Construct such a pair and explain what extra word would distinguish them.
22. Design a number code where two different words share the same code, and explain why letter-sum codes cannot be reversed uniquely.

I · Previous year exam style

23. LOUNGE is coded as 80 and PARCEL as 61. What is the code for ZEALOT? PYQ 2025 · Shift 1
24. MATTER is coded as 83 and SOLIDS as 84. What is the code for LIQUID? PYQ 2025 · Shift 2
25. ABOUT is written as YYRDB and ACUTE as JXXEB. How will ANGLE be written? PYQ 2021 · Shift 2
26. 'Tudo Bem' is 'All Fine', 'Como Esta' is 'How You', 'Bem Como' is 'Fine You'. How is 'Tudo Esta' written? PYQ 2021 · Shift 3
27. PARENTS relates to TEVIRXW and ACHIEVE to EGLMIZI. To what does PROUDLY relate? PYQ 2025 · Shift 1

J · Mixed revision test

28–37. Ten mixed questions across all five code types, timed at seven minutes total. Full set with answer key is in the free PDF.
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Three marks decoded. Twelve reasoning topics still on the table.

Live classes cover every reasoning, aptitude, English and GK topic with the same method — find the rule, prove it on two words, then apply. Fees are kept low on purpose.