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4.4 Coding-Decoding, Cipher Patterns & Symbol Operations
Ateneo College Entrance Test ACET
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1 Chapter 1: Mathematics
1.1 Real Numbers, Ratios, Rates & Percentages 1.2 Algebraic Expressions, Polynomials & Linear Equations 1.3 Functions, Domain/Range, Graphs & Transformations 1.4 Quadratic, Polynomial, Exponential & Logarithmic Equations 1.5 Plane Geometry: Triangles, Circles, Polygons & Perimeter/Area 1.6 Coordinate Geometry: Lines, Distance, Midpoints & Conic Sections 1.7 Trigonometry: Right Triangle Ratios, Unit Circle & Basic Identities 1.8 Arithmetic & Geometric Sequences, Series & Word Patterns 1.9 Permutations, Combinations, Probability & Statistics
2 Chapter 2: English Proficiency
2.1 Subject-Verb Agreement, Verb Tenses & Aspect 2.2 Pronoun-Antecedent Agreement, Case, Misplaced & Dangling Modifiers 2.3 Sentence Structure, Run-Ons, Fragments & Parallelism 2.4 Contextual Vocabulary, Word Roots, Prefixes & Suffixes 2.5 Advanced Synonyms, Antonyms & Nuanced Vocabulary 2.6 Verbal Analogies: Relationship Types & Solving Strategies 2.7 Punctuation, Capitalization, Mechanics & Common Errors 2.8 Diction, Idiomatic Expressions, Prepositions & Frequently Confused Words
3 Chapter 3: Reading Comprehension
3.1 Identifying Main Ideas, Central Themes & Paragraph Summaries 3.2 Locating Explicit Details, Supporting Evidence & Data 3.3 Drawing Logical Inferences & Unstated Conclusions 3.4 Analyzing Author's Purpose, Point of View, Tone & Attitude 3.5 Interpreting Figurative Language, Tone Words & Context Clues 3.6 Text Structure, Rhetorical Devices & Evaluating Arguments
4 Chapter 4: Logical and Abstract Reasoning
4.1 Number & Letter Series Patterns & Formulas 4.2 Abstract Reasoning: Matrix Patterns & Figure Rotations 4.3 Formal Syllogisms, Categorical Logic & Deductive Proofs 4.4 Coding-Decoding, Cipher Patterns & Symbol Operations 4.5 Spatial Visualization, Paper Folding & Venn Diagram Logic
5 Chapter 5: General Knowledge
5.1 Philippine History, Government, Constitution & Civics 5.2 Integrated Science: Biology, Chemistry, Physics & Earth Science 5.3 Philippine & World Geography, Basic Economics & Cultural Facts 5.4 Current Events, World Landmarks, Literature & General Trivia
6 Chapter 6: ACET Essay Writing & Exam Strategies
6.1 ACET Essay: Thesis Development, Structuring & Argumentation 6.2 Time Allocation, Pacing Strategies & Subtest Tactics 6.3 Guessing Strategies (No Penalty), Test Anxiety & Exam Day Readiness
4.4 Coding-Decoding, Cipher Patterns & Symbol Operations
Key Takeaways Explain This Topic AI
Solve letter-to-letter, letter-to-number, and direct substitution ciphers using position mapping and constant/variable shift algorithms.
Decode artificial language and symbolic logic problems by isolating recurring morphemes and structural syntax.
Master non-standard operator definition problems (e.g., a ⊗ b = a² - 3b + 1) by strict order of operations and variable substitution.
Utilize frequency analysis, word-length constraints, and boundary letter checks to decode word ciphers rapidly under time constraints.
Last updated: July 2026
Coding-Decoding, Cipher Patterns & Symbol Operations
Coding-decoding and symbol manipulation items on the ACET evaluate symbolic processing agility, rule application, and working memory. These questions present encrypted words, artificial language translations, or novel mathematical operators. Rather than relying on trial-and-error, you must approach cipher breakdown systematically using position mapping, morphological alignment, and operator evaluation formulas.
1. Classical Cipher Classification & Decryption Rules
In cryptography items, plaintext letters are transformed into ciphertext letters or numbers via deterministic encoding algorithms.
1. Caesar Shift & Variable-Shift Ciphers
Every letter is shifted forward or backward in the alphabet by a specified value k k k : C i = ( P i + k − 1 ( m o d 26 ) ) + 1 C_i = (P_i + k - 1 \pmod{26}) + 1 C i = ( P i + k − 1 ( mod 26 )) + 1
Constant Shift: Every letter moves by + k +k + k (e.g., + 3 ⟹ A → D , B → E +3 \implies A \rightarrow D, B \rightarrow E + 3 ⟹ A → D , B → E ).
Progressive Shift: The shift increases arithmetically per letter position: + 1 , + 2 , + 3 , + 4 , … +1, +2, +3, +4, \dots + 1 , + 2 , + 3 , + 4 , …
Plaintext HELL → H ( + 1 ) E ( + 2 ) L ( + 3 ) L ( + 4 ) ⟹ I , G , O , P \rightarrow H(+1)E(+2)L(+3)L(+4) \implies I, G, O, P → H ( + 1 ) E ( + 2 ) L ( + 3 ) L ( + 4 ) ⟹ I , G , O , P .
Alternating Shift: Alternates between + k 1 +k_1 + k 1 and − k 2 -k_2 − k 2 (e.g., + 2 , − 1 , + 2 , − 1 +2, -1, +2, -1 + 2 , − 1 , + 2 , − 1 ).
2. Atbash Complementary Cipher (Reverse Alphabetic Mapping)
Each letter is mapped to its complementary opposite position in the 26-letter alphabet: Position ( C i ) + Position ( P i ) = 27 \text{Position}(C_i) + \text{Position}(P_i) = 27 Position ( C i ) + Position ( P i ) = 27
Mapping pairs: A ↔ Z , B ↔ Y , C ↔ X , D ↔ W , … , M ↔ N A \leftrightarrow Z, B \leftrightarrow Y, C \leftrightarrow X, D \leftrightarrow W, \dots, M \leftrightarrow N A ↔ Z , B ↔ Y , C ↔ X , D ↔ W , … , M ↔ N .
Plaintext CAT ⟹ C ( 3 ) → X ( 24 ) , A ( 1 ) → Z ( 26 ) , T ( 20 ) → G ( 7 ) ⟹ \implies C(3) \rightarrow X(24), A(1) \rightarrow Z(26), T(20) \rightarrow G(7) \implies ⟹ C ( 3 ) → X ( 24 ) , A ( 1 ) → Z ( 26 ) , T ( 20 ) → G ( 7 ) ⟹ XZG .
3. Block Reversal & Structural Transposition
Transposition ciphers rearrange letter order without altering letter identities:
Word Halving: Split word into two equal halves and reverse each half.
MONKEY → M O N ∣ K E Y → N O M ∣ Y E K ⟹ \rightarrow MON \mid KEY \rightarrow NOM \mid YEK \implies → MON ∣ K E Y → NOM ∣ Y E K ⟹ NOMYEK .
Odd-Even Index Swap: Swap adjacent letter pairs: P 1 ↔ P 2 , P 3 ↔ P 4 P_1 \leftrightarrow P_2, P_3 \leftrightarrow P_4 P 1 ↔ P 2 , P 3 ↔ P 4 .
MATH → \rightarrow → AMHT .
2. Letter-to-Number Encoding Systems
Number coding maps letters to numerical values based on explicit algebraic formulas. LETTER-TO-NUMBER CODING SCHEMES
- |
- +-----------------------+-----------------------+
- | |
- v v
- Direct Index Sum Weighted / Scaled Code
- (Sum of A=1...Z=26) (Vowels ×2, Consonants +1)
- Example: CAT Example: CAT
- C=3, A=1, T=20 C(4) + A(2) + T(21)
- Sum = 3+1+20 = 24 Sum = 4+2+21 = 27
- Common ACET Numeric Encoding Formulas
Direct Positional Sum: Code = ∑ i = 1 n Pos ( L i ) \text{Code} = \sum_{i=1}^n \text{Pos}(L_i) Code = ∑ i = 1 n Pos ( L i ) .
Opposite Positional Sum: Code = ∑ i = 1 n ( 27 − Pos ( L i ) ) \text{Code} = \sum_{i=1}^n (27 - \text{Pos}(L_i)) Code = ∑ i = 1 n ( 27 − Pos ( L i )) .
Length Multiplied Index: Code = ( ∑ Pos ( L i ) ) × Word Length \text{Code} = \left(\sum \text{Pos}(L_i)\right) \times \text{Word Length} Code = ( ∑ Pos ( L i ) ) × Word Length .
3. Decoding Artificial Languages (Synthetic Syntax)
Artificial language questions present translated word pairs and require decoding unknown phrases. Use the Morphological Alignment Algorithm to isolate vocabulary:
Step-by-Step Translation Algorithm
Given the synthetic phrases:
"pina loma" = "blue house"
"pina kuta" = "blue car"
"tivo kuta" = "fast car"
Isolate Overlapping Words:
Compare Phrase 1 & Phrase 2: The word "pina" appears in both synthetic strings, and "blue" appears in both English meanings. ⟹ \implies ⟹ "pina" = "blue" .
Compare Phrase 2 & Phrase 3: The word "kuta" appears in both synthetic strings, and "car" appears in both English meanings. ⟹ \implies ⟹ "kuta" = "car" .
Deduce Remaining Vocabulary:
From Phrase 1: Since "pina" = "blue" , then "loma" = "house" .
From Phrase 3: Since "kuta" = "car" , then "tivo" = "fast" .
Determine Structural Syntax (Modifier Order):
In "pina loma" ( "blue house" ), "pina" (modifier) comes first, followed by "loma" (noun). Syntax order matches English (Modifier + Noun).
Synthesize Target Phrase:
To translate "fast house" : Modifier ( "fast" = "tivo" ) + Noun ( "house" = "loma" ) ⟹ \implies ⟹ "tivo loma" .
4. Custom Symbol Operations & Non-Standard Algebra
ACET symbol operation items invent custom arithmetic operators defined by algebraic expressions. Treat these as function evaluations.
- Evaluation Rules
- Definition: a ⊗ b = a 2 − 3 b + 1 a \otimes b = a^2 - 3b + 1 a ⊗ b = a 2 − 3 b + 1
Non-Commutative Property: a ⊗ b ≠ b ⊗ a a \otimes b \neq b \otimes a a ⊗ b = b ⊗ a . Always preserve left/right variable placement.
Order of Precedence: Evaluate expressions inside parentheses first.
Nested Symbol Walkthrough
Evaluate ( 4 ⊗ 2 ) ⊗ 3 (4 \otimes 2) \otimes 3 ( 4 ⊗ 2 ) ⊗ 3 using a ⊗ b = a 2 − 3 b + 1 a \otimes b = a^2 - 3b + 1 a ⊗ b = a 2 − 3 b + 1 :
Step 1: Evaluate Inner Bracket ( 4 ⊗ 2 ) (4 \otimes 2) ( 4 ⊗ 2 ) :
Let a = 4 a = 4 a = 4 and b = 2 b = 2 b = 2 .
4 ⊗ 2 = ( 4 ) 2 − 3 ( 2 ) + 1 = 16 − 6 + 1 = 11 4 \otimes 2 = (4)^2 - 3(2) + 1 = 16 - 6 + 1 = 11 4 ⊗ 2 = ( 4 ) 2 − 3 ( 2 ) + 1 = 16 − 6 + 1 = 11 .
Step 2: Evaluate Outer Expression ( 11 ⊗ 3 ) (11 \otimes 3) ( 11 ⊗ 3 ) :
Let a = 11 a = 11 a = 11 and b = 3 b = 3 b = 3 .
11 ⊗ 3 = ( 11 ) 2 − 3 ( 3 ) + 1 = 121 − 9 + 1 = 113 11 \otimes 3 = (11)^2 - 3(3) + 1 = 121 - 9 + 1 = 113 11 ⊗ 3 = ( 11 ) 2 − 3 ( 3 ) + 1 = 121 − 9 + 1 = 113 .
5. Rapid Cryptanalytic Inspection Summary
Cipher Type Primary Identifier Diagnostic Action Key Counter-Strategy
Atbash / Inverse Word length preserved; letter pairs add to 27 Check P 1 + C 1 = 27 P_1 + C_1 = 27 P 1 + C 1 = 27 Test first & last letters instantly
Caesar Shift Fixed letter distance across all positions Compute Pos ( C i ) − Pos ( P i ) \text{Pos}(C_i) - \text{Pos}(P_i) Pos ( C i ) − Pos ( P i ) Verify wrap-around at Z -> A
Transposition Letters in ciphertext are identical to plaintext Count letter frequencies Split word into sub-blocks