Reasoning Ability - Lesson 6

Stop guessing the code. Find the rule.

Coding-Decoding is a rule-detection machine: a word goes in, a hidden transformation runs, a code comes out. Learn to spot the rule that survives every letter.

Learning time
20 min · self-paced
Exam weight
3-5 questions / set
Sections
9 modules
Input
B
A
N
K
Hidden rule
SHIFT +1
each letter +1
Code
C
B
O
L
Topic map

One machine, nine kinds of rule.

Every question is the same shape - input, hidden rule, output. These nine rule families teach you to recognize which rule is running.

The mental modelInput → hidden rule → coded output. Decoding just runs the machine backward.
Input
C
O
D
E
Hidden rule
SHIFT +1
the hidden rule
Code
D
P
E
F
Rule 01

Alphabet positions

A=1 to Z=26, vowels, and the M/N midpoint anchors.

Rule 02

Letter shifts

Constant, alternating, increasing, and cyclic shifts.

Rule 03

Reverse alphabet

Mirror pairs A↔Z where positions add to 27.

Rule 04

Rearrangement

Letters unchanged - only their order moves.

Rule 05

Number coding

Sum, product, position, length and place-value codes.

Rule 06

Symbol substitution

Build a mapping key: letters ↔ @, #, %, $.

Rule 07

Coded language

Match common words to common code tokens.

Rule 08

Mixed & conditional

Separate layers; apply rules only when conditions hold.

Checkpoint 09

Mastery check

Mini test + alphabet-strip cheat sheet to lock it in.

Foundation - 01

Seven rule families. Learn to recognize each on sight.

Every code belongs to one of these. Tap through to see the rule, what it guarantees, and the trap that catches most learners.

Interactive
Alphabet position values

The base tool: each letter has a number, A=1 up to Z=26. Vowels sit at 1, 5, 9, 15, 21; M and N mark the midpoint. Use it as one lens - not the only one.

Use it
Forward count from A=1. The midpoint split at M/N helps you jump quickly to the back half.
Watch out
Off-by-one: do not start counting A as 0. A is always 1 unless the question redefines it.
A
1
B
2
C
3
D
4
E
5
F
6
G
7
H
8
I
9
J
10
K
11
L
12
M
13
N
14
O
15
P
16
Q
17
R
18
S
19
T
20
U
21
V
22
W
23
X
24
Y
25
Z
26
Try it yourself

Pick the rule and watch the code build letter by letter.

Select a coding rule, run it on a sample word, and watch each character transform so the hidden pattern becomes visible instead of guessed.

Live sandbox
Coding rule
Input word
Rule: Each letter shifts one step forward in the alphabet.
BANK becomes CBOL.
B
C
A
B
N
O
K
L
One verified transformation must hold across every position. If it breaks on any letter, the rule is wrong.
Method - 02

Compare, hypothesize, verify, apply, re-check.

Do not guess the pattern - prove the rule, then apply it cleanly. This loop works on every coding type.

STEP 1

Compare

Write input and code in two aligned rows so every position lines up. Identify the coding type first.

STEP 2

Hypothesize

Test the easiest rules first: shift, reverse, position-value, rearrangement, sum, substitution.

STEP 3

Verify

Check the rule across every letter, word, or example. Reject any rule that works only once.

STEP 4

Apply

Run the verified rule on the target - or reverse it if the question asks you to decode.

STEP 5

Re-check

Confirm against the options and the direction: did they ask to encode or to decode?

Pro tip. Prefer the simplest rule that survives every letter. A complicated rule that fits only one example is the classic overfitting trap.
Question types - 03

The 8 formats every exam recycles.

Name the family in the first five seconds and you already know which rule to test first.

Simple letter shift

~40 sec
What it looks like
BANK → CBOL. Each coded letter is the original moved a fixed number of steps.
How to identify
Letters look "close" to the originals - one or two steps along the alphabet.
How to solve
Write the shift above every position. If all are equal, apply that shift to the target word.
Mini example. BANK → CBOL is +1 each. So LOAN → MPBO.
Trap: Assuming the whole word follows the first letter's shift. Check every position.

Reverse alphabet coding

~45 sec
What it looks like
Each letter is replaced by its A↔Z mirror. MANGO → NZMTL.
How to identify
Coded letters look "far" from the originals, and position-pairs add to 27.
How to solve
Map each letter to its mirror. Works identically both ways.
Mini example. M↔N, A↔Z, N↔M, G↔T, O↔L → MANGO becomes NZMTL.
Trap: Treating the mirror of A as 26 instead of the letter Z.

Alternating / increasing shift

~70 sec
What it looks like
Shifts differ by position: +1, +2, +3 or +1, -1, +1, -1.
How to identify
The per-letter shifts form a pattern instead of a constant.
How to solve
Detect the shift sequence, then continue it across the target word.
Mini example. If shifts read +1, +2, +3, +4 then the 5th letter shifts +5.
Trap: Stopping after two letters. Confirm the sequence with at least three positions.

Word rearrangement

~35 sec
What it looks like
TRAIN → NIART. The letters are identical; only the order changed.
How to identify
Same letter set in input and output. No new letters appear.
How to solve
Find the reorder rule - full reverse, first-last swap, odd/even shuffle - then apply it.
Mini example. TRAIN → NIART is a full reverse.
Trap: Hunting for letter shifts when nothing was actually shifted.

Number coding

~55 sec
What it looks like
A word maps to a number: TIGER → 59.
How to identify
The code is digits, not letters. Test sum, product, count, or place value.
How to solve
Convert each letter to its position, then apply the operation the example reveals.
Mini example. TIGER = 20+9+7+5+18 = 59. HORSE = 65.
Trap: Guessing the operation. Verify it reproduces the given code exactly first.

Symbol substitution

~50 sec
What it looks like
Letters or numbers replaced by @, #, %, $ via a fixed key.
How to identify
A clear one-to-one mapping table is given or implied.
How to solve
Build the substitution key, then read the answer straight off it.
Mini example. If A=@, B=#, C=% then CAB → %@#.
Trap: Operation swaps - sometimes + is redefined to mean -.

Coded language

~80 sec
What it looks like
Whole sentences in code. "red blue green = ka mi tu."
How to identify
Words map to word-tokens; there is no alphabet pattern at all.
How to solve
Compare sentences, match shared words to shared codes, isolate each token.
Mini example. Two sentences sharing "red" and "blue" must share the codes ka and mi.
Trap: Looking for letter shifts. This is pure overlap matching.

Mixed & conditional

~90 sec
What it looks like
Letters, digits and symbols together - or rules that apply only under conditions.
How to identify
Multiple layers in one code, or if-then instructions.
How to solve
Separate into layers and solve each in turn.
Mini example. A3# = letter A shifted +3, then an order operation - solved layer by layer.
Trap: Mixing layers together instead of resolving them one at a time.
Worked examples - 04

Four codes cracked, step by step.

One per major rule family. Step through the reasoning - the answer locks on the final step.

Problem
QuestionIf BANK is coded as CBOL, how will LOAN be coded?
Answer
? ? ?
Run the decoder
B
?
·
A
?
·
N
?
·
K
?
·
Step 1. Write BANK and CBOL in aligned columns to compare each position.
1 / 4
Common traps - 05

The 8 mistakes that turn easy marks into wrong answers.

Tap any card to flip from the wrong instinct to the correction.

Trap 01 - First-letter trap
B→C is +1, so the whole word is +1.
Tap for the fix
Trap 02 - Encode vs decode
Apply the rule forward, even to decode.
Tap for the fix
Trap 03 - Reverse confusion
Z is 26, so the reverse of A is 26.
Tap for the fix
Trap 04 - Off-by-one
Start counting A as 0, so B = 1.
Tap for the fix
Trap 05 - Overfitting
A complex rule fits one example, so it is right.
Tap for the fix
Trap 06 - Order vs shift
The output looks different - letters must have changed.
Tap for the fix
Trap 07 - Vowel/consonant miss
Treat every letter the same.
Tap for the fix
Trap 08 - Option trap
Pick the closest-looking option.
Tap for the fix
Best practices - 06

Six exam-room habits that prevent silly losses.

Small disciplines that make the rule visible instead of guessed.

TIP 01
Align two rows

Write original and code in two aligned rows. Most patterns become visible when positions line up.

TIP 02
Mark the shift above

For letter codes, write +1, +2, -1 above each position. The sequence reveals the rule.

TIP 03
Letters same? It is order

If every original letter is still present, stop hunting shifts - it is rearrangement.

TIP 04
A=1 only when it fits

Use position values when the code clearly suggests number logic - not by reflex.

TIP 05
Underline shared words

In coded language, underline common words and circle common tokens to match them.

TIP 06
Check the direction last

Before answering, confirm whether they want the code, the original word, a missing code, or a language meaning.

Mini practice - 07

Decode 4 yourself - instant feedback included.

Mixed difficulty, no timer. Every answer comes with a worked explanation and a diagram.

Question 1 of 4Easy
Score - 0/4
If CAT is coded as DBU, how is DOG coded?
Streak target: 3 in a row.
Cheat sheet - 08

One screenshot to revise the whole topic.

The alphabet strip plus the rules that crack most codes.

Alphabet strip - A=1 to Z=26
A
1
B
2
C
3
D
4
E
5
F
6
G
7
H
8
I
9
J
10
K
11
L
12
M
13
N
14
O
15
P
16
Q
17
R
18
S
19
T
20
U
21
V
22
W
23
X
24
Y
25
Z
26
Vowels: 1, 5, 9, 15, 21 Midpoint: M=13, N=14Mirror pairs add to 27
Rule families at a glance
FamilySignalExample
Shiftletters look closeBANK→CBOL (+1)
Reversepairs sum to 27A↔Z, M↔N
Rearrangesame letter setTRAIN→NIART
Numbercode is digitsTIGER→59
Symbol@ # % $A=@, B=#
Languageword↔wordblue=mi
The exam-time process
  • 01Align input and code in two rows.
  • 02Ask whether letters changed, or only the order.
  • 03Test the simplest rules first.
  • 04Verify across every letter or example.
  • 05Apply forward to encode, backward to decode.
  • 06Re-check the direction the question wants.
Do not guess the pattern - prove the rule, then apply it cleanly.
What's next - 09

Lesson done. Time to lock it in.

Practice the hard stuff, queue the next topic, or revisit what tripped you up.

Practice 20 coding questions

Adaptive difficulty across all rule families, instant explanations, mistakes auto-saved. ~18 minutes.

Start practice

Try a code-language set

10 overlap-matching puzzles - the highest-yield Mains format.

Open set

Revisit mistakes

Re-drill the first-letter and overfitting traps - the two costliest errors.

Open notebook

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