Letter Shift
Move alphabet positions by a fixed, changing or alternating value.
Note 21
Coding, Decoding and Word Building
Complete notes for SSC Combined Graduate Level examinations
1The Big Picture — Graphic Mind Map
Position / Number
Convert letters into direct or reverse positions; then apply arithmetic.
Substitution
Replace each letter, number, word or relation with a consistent code.
Matrix / Table
Locate a character through row–column, coordinate or keyed table rules.
Sentence Language
Common words across statements reveal common code tokens.
Conditional Code
Choose the applicable rule from properties such as vowel, parity, position or case.
Word Building
Respect the exact letter inventory, frequency, case and arrangement conditions.
Dictionary Order
Compare from the first unequal letter; a completed prefix comes first.
1. Identify
code family
➜code family
2. Convert
letters / symbols
➜letters / symbols
3. Compare
position-wise
➜position-wise
4. Infer
one consistent rule
➜one consistent rule
5. Reverse-check
decode fully
decode fully
2The Foundation — Basics to Expert Coding Logic
2.1 What Coding Means
Encoding transforms an original item into another representation. Decoding reverses or reconstructs that transformation.
A good rule is consistent, reversible where required, and position-aware. The exam asks you to infer the hidden rule—not to use real cryptography.
2.2 Alphabet Position Toolkit
\[A=1,B=2,\ldots,Z=26\]
If direct position is \(p\), reverse position is:
\[p_{\mathrm{rev}}=27-p\]
Thus \(A\leftrightarrow Z\), \(B\leftrightarrow Y\), and every opposite pair sums to \(27\).
2.3 Master Classification of Codes
| Code family | Operation | Primary clue | First action |
|---|---|---|---|
| Letter shift | Forward/backward alphabet movement | Word length and positions preserved | Write positional differences |
| Substitution / permutation | Replace or rearrange characters | Same letters recur in new places/codes | Map input to output position-wise |
| Number coding | Positions become a number through sum/product/rule | Word maps to one or more numbers | Convert letters to positions |
| Symbol coding | Character/class maps to symbol | Symbols replace letters, digits or relations | Build a mapping table |
| Matrix / coordinate | Row–column location encodes item | Grids, two-digit coordinates, table keys | Identify coordinate order |
| Conditional | Different rule selected by a stated property | “If…otherwise…” clauses | Test conditions in stated priority |
| Sentence / artificial language | Words correspond to code tokens | Multiple coded statements overlap | Intersect common words and tokens |
| Word building / order | Inventory, rearrangement or lexicographic comparison | Meaningful word, positions, dictionary | Count letters or compare first mismatch |
2.4 Fixed Letter Shift
For a forward shift \(k\), use cyclic positions:
\[p'=((p-1+k)\bmod 26)+1\]
Example: \(CAT\xrightarrow{+3}FDW\). Decoding applies \(-3\).
C➜FA➜DT➜W
2.5 Changing & Alternating Shifts
Shifts may form \(+1,+2,+3,\ldots\), alternate \(+2,-2,+2,-2,\ldots\), or depend on position \(i\).
Write a shift row beneath the letters. A sequence of shifts is often the real pattern.
2.6 Mirror / Reverse Alphabet
Replace each position \(p\) by \(27-p\).
Example: \(BAD\to YZW\), because \(B\to Y\), \(A\to Z\), \(D\to W\).
Mirror substitution changes letters; reversing a word changes their order. They are different operations.
2.7 Rearrangement Codes
The output may reverse, rotate, swap pairs, or follow an index permutation.
If output order is \((3,1,4,2)\), then \(TEAM\to ATME\).
Track where each input position goes; do not search for alphabet shifts first.
2.8 Direct Substitution
A mapping such as \(G\mapsto Q\) must be reused wherever \(G\) occurs. Repeated input characters should normally yield repeated outputs under simple substitution.
Create a two-row key instead of holding mappings mentally.
2.9 Direct Position Coding
Each letter may be replaced by direct or reverse position:
\[D=4,\qquad D_{\mathrm{rev}}=23\]
Small and capital letters may share positions unless the question explicitly assigns separate classes.
2.10 Number Coding of Whole Words
Common arithmetic generators
- Sum: \(S=\sum_{i=1}^{m}p_i\)
- Product or selected-position product
- First plus last, or first minus last
- Sum of vowels/consonants separately
- Average: \(\bar p=S/m\)
- Weighted sum: \(\sum i p_i\)
How to infer the generator
Convert the word into positions and test the simplest relation.
For \(CAT\), position sum is \(3+1+20=24\). But never assume “sum” until another example confirms it.
A single word–number pair cannot uniquely determine a rule.
2.11 Symbol Codes
Digits, letters, operators or relations may be replaced by symbols. First construct a legend such as \(5\mapsto\#\).
Keep identity and operation separate: a symbol can stand for a value or for an action.
2.12 Matrix / Coordinate Codes
A code \(rc\) may mean row \(r\), column \(c\). Some questions reverse it to \(cr\) or use two alternative matrices.
Verify coordinate order using at least two known entries.
2.13 Conditional Coding
Apply conditions in the stated order. A typical hierarchy is:
- test a special condition;
- if false, test the next;
- otherwise use the default rule.
If two conditions are true, stated priority decides.
2.14 Sentence / Artificial-Language Coding
Intersection principle
If two sentences share exactly one word and their code lists share exactly one token, those common items correspond.
“red flower blooms” → ka mi zo
“red sun rises” → ka tu pe
Therefore red → ka.
Elimination principle
After fixing common pairs, cancel them from every statement. Remaining unmatched words and tokens form smaller one-to-one sets.
Order is usually irrelevant unless the question explicitly preserves order.
Set view: for sentence word-set \(W_i\) and token-set \(C_i\), unique intersections \(W_1\cap W_2\) and \(C_1\cap C_2\) reveal a pair. Multiple common items require another statement.
2.15 Word Building — Letter Inventory Logic
Frequency rule
A candidate word is possible only if each letter count is available:
\[f_{\mathrm{candidate}}(x)\le f_{\mathrm{source}}(x)\quad\text{for every letter }x\]
Repeated letters must be counted, not merely noticed.
Positional conditions
Questions may fix first/last letters, demand adjacency, separation, vowels at certain places, or unchanged relative order.
“Using letters of” permits rearrangement; “without changing order” permits only a subsequence.
Case classification
Uppercase and lowercase can be distinct symbols when the problem states case-sensitive coding. Otherwise, word formation normally ignores case.
Never infer case significance without evidence.
2.16 Dictionary Order & Letter Positions
Lexicographic algorithm
- Compare first letters.
- If equal, move right until the first mismatch.
- The smaller alphabet position comes first.
- If one word ends while all compared letters match, the shorter prefix comes first.
Thus \(CAR\lt CARE\lt CART\lt CAT\) in dictionary order.
Position after rearrangement
Maintain two labels: original position and new position. If a word has length \(m\), the position from the right of the item at left-position \(i\) is:
\[i_{\mathrm{right}}=m-i+1\]
For central positions, odd \(m\) gives one centre; even \(m\) gives two.
2.17 Expert Edge Cases
| Situation | Correct interpretation | Why candidates err |
|---|---|---|
| Repeated input letter, different output | Simple substitution is unlikely; position-dependent rule may operate | They force a one-to-one key |
| Output word has same length | Could be shift, mirror, rearrangement or position-wise mixed rule | They assume only Caesar shift |
| Two common words and two common tokens | Pairs remain ambiguous without another statement | They assign by visual order |
| Two-digit coordinate | Could be row–column or column–row | They never calibrate the grid |
| Conditional rules overlap | Follow stated priority or exclusivity wording | They apply every true rule |
| Candidate uses repeated letter | Check multiplicity against source inventory | Set membership hides frequency |
| One word is prefix of another | Shorter complete word precedes longer one | They compare an absent next letter |
| Alphabet crosses \(Z\) | Wrap only when the pattern is cyclic | They stop or wrap automatically |
3Short Tricks & Magic Formulas — TCS Speed Tools
3.1 Four Anchors
Memorise \(A=1\), \(M=13\), \(N=14\), \(Z=26\). Derive all nearby positions instead of recounting.
3.2 Mirror in One Step
Opposite position is \(27-p\). This instantly handles reverse-alphabet codes and mirror pairs.
3.3 Vertical Difference Row
Write input above output, compare each column, and record signed cyclic shifts. Constant, progressive or alternating patterns become visible.
3.4 Position Map First
If the output contains the same characters, mark original indices. Test reversal, pair swap, rotation and odd–even collection before alphabet arithmetic.
3.5 Common–Common Rule
Common word ↔ common token. Use set intersection, then cancel confirmed pairs everywhere.
3.6 Calibrate Coordinates
Use two known symbols to decide whether a two-digit code means \((r,c)\) or \((c,r)\). Never trust the display order.
3.7 First-Mismatch Pencil Mark
In dictionary order, underline the first unequal letters only. Ignore every character after that decision point.
3.8 Inventory Tally
For word building, tally only repeated or scarce letters. Reject a candidate at the first frequency excess.
3.9 Condition Priority
Turn prose into a decision tree. Once an exclusive condition matches, stop; use the default only if none match.
3.10 Decode to Confirm
After finding an encoding rule, reverse it on a known example. A rule that cannot reconstruct the input is suspect.
3.11 Right-Position Formula
For length \(m\), left-position \(i\) corresponds to right-position \(m-i+1\). This avoids manual recounting.
3.12 Option-Led Elimination
When several rules partly fit, test the options against the most restrictive known position, repeated letter or condition first.
3.13 Compact Formula & Procedure Bank
| Need | Formula / procedure | Speed cue |
|---|---|---|
| Direct position | \(A=1,\ldots,Z=26\) | Use four anchors |
| Reverse position | \(p_{\mathrm{rev}}=27-p\) | Mirror makes \(27\) |
| Cyclic forward shift | \(p'=((p-1+k)\bmod26)+1\) | Wrap after \(Z\) |
| Cyclic backward shift | \(p'=((p-1-k)\bmod26+26)\bmod26+1\) | Add \(26\) before remainder |
| Position from right | \(m-i+1\) | Length plus one minus left position |
| Word feasibility | \(f_c(x)\le f_s(x)\) for every \(x\) | Count duplicates first |
| Sentence code | Intersect common word/token sets | Common ↔ common |
| Dictionary order | Compare the first unequal position | Prefix ends first |
4The SSC / TCS Traps — Red Flags
🚩 4.1 Wrap Error
A forward shift beyond \(Z\) may cycle to \(A\). But apply wrap only when the rule is alphabetic and cyclic.
🚩 4.2 Mirror vs Reverse
Word reversal changes order; alphabet mirror substitutes letters. \(AB\to BA\) and \(AB\to ZY\) are not the same.
🚩 4.3 Ambiguous Intersections
Two common words and two common codes do not identify exact pairs. A third statement is necessary.
🚩 4.4 Row–Column Reversal
Code \(23\) may mean row \(2\), column \(3\), or the reverse. Calibrate before reading the table.
🚩 4.5 Duplicate-Letter Blindness
A source containing one \(E\) cannot form a candidate needing two \(E\)'s, even though the letter is present.
🚩 4.6 Prefix Rule Forgotten
If all letters of the shorter word match the start of the longer word, the shorter word comes first.
🚩 4.7 Applying Two Conditions
When rules are mutually exclusive, stop after the first matched condition. Stacking them creates a distractor.
🚩 4.8 Broken One-to-One Mapping
Under simple substitution, the same input must keep the same output. If it changes, inspect position or context.
🚩 4.9 Assuming Position Sum
One word–number pair supports many formulas. Confirm sum, product or endpoint rule with another example.
🚩 4.10 Inventing Case Rules
Capital and small letters are separate only when stated or demonstrated. Typography alone may be decorative.
🚩 4.11 Losing Original Positions
After rearrangement, candidates often answer with the new index when the question asks for the original one. Label both.
🚩 4.12 Local Pattern Overfit
A clever relation fitting one pair is not enough. Verify every known example, repeated character and output position.
TCS decision rule: prefer the simplest transformation that respects every sample and wording condition. Do not repair an inconvenient example by changing the rule halfway.
5Memory Hooks & Mnemonics
5.1 “SMART” Code Scan
Shift, Mirror, Arrange, Replace, Total. Test in this order.
5.2 “Mirror Makes 27”
Opposite alphabet positions always total \(27\). See a mirror code—subtract from \(27\).
5.3 “Common Meets Common”
In sentence coding, intersect words and tokens before making any pairing.
5.4 “Letters Are Coins”
You cannot spend a letter more times than the source word owns it. Count repeated coins.
5.5 “First Fight Wins”
In dictionary order, the first unequal letter decides. If no fight occurs and one word ends, the shorter wins.
5.6 “Say the Coordinate Aloud”
Before reading \(23\), say “row two, column three”—then verify the convention.
5.7 “First True, Then Stop”
For priority conditions, take the first applicable branch and do not stack later rules.
5.8 “Turn the Key Back”
Decode a known result. A correct key must take you back to the original without exceptions.
Code Recognition Map
- Same length and similar positions → shift or mirror.
- Same characters, new order → permutation.
- Whole word becomes number → position arithmetic.
- Overlapping coded statements → set intersection.
- Grid or two-digit labels → coordinates.
Word Reasoning Map
- Can it be formed? → frequency inventory.
- Order unchanged? → subsequence, not anagram.
- Dictionary? → first mismatch / prefix rule.
- From right? → \(m-i+1\).
- Case mentioned? → classify capital/small separately.
Final recall line: “Classify the code, map the positions, preserve every condition, and reverse-check the result.”