{"id":9164,"date":"2026-06-01T21:33:48","date_gmt":"2026-06-01T21:33:48","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=9164"},"modified":"2026-06-01T21:33:48","modified_gmt":"2026-06-01T21:33:48","slug":"decryption-of-patterns","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/decryption-of-patterns\/","title":{"rendered":"Decryption Of Patterns"},"content":{"rendered":"

Unit: <\/strong>Coding & Decoding<\/strong><\/h2>\n

Chapter: <\/strong>Decryption of Patterns<\/strong><\/h3>\n

Reference: – Introduction to Decryption, Pattern Recognition in Letter Codes, Pattern Recognition in Number Codes, Mixed Alphanumeric Patterns, Positional Value Decryption, Mathematical Operation Decryption, Sequence and Series Based Decryption<\/em><\/p>\n

After studying this chapter, you should be able to understand:<\/strong><\/p>\n

    \n
  • Introduction to Classification<\/li>\n
  • The fundamental concept of decryption in coding-decoding.<\/li>\n
  • How to recognize consistent patterns in letter and number codes.<\/li>\n
  • Techniques for decrypting codes based on positional values and mathematical operations.<\/li>\n
  • Applying sequence and series logic to break complex codes.<\/li>\n<\/ul>\n

    Introduction to Decryption<\/strong><\/p>\n

    Definition<\/u><\/strong><\/p>\n

    Decryption is the reverse process of encryption. In logical reasoning, it refers to the method of deciphering or decoding a given pattern to find the original word, number, or message from its coded form.<\/p>\n

    The core of decryption lies in identifying the hidden rule or pattern that connects the original item to its code. Once the rule is found, it can be applied to decode other items or to find the odd one out.<\/p>\n

    Importance of Decryption<\/u><\/strong><\/p>\n

      \n
    • Sharpens analytical and logical thinking skills.<\/li>\n
    • Essential for solving coding-decoding problems in competitive exams.<\/li>\n
    • Forms the basis for understanding cryptography and data security concepts.<\/li>\n
    • Improves mental agility and the ability to recognize abstract patterns.<\/li>\n<\/ul>\n

      Example<\/strong><\/p>\n

      Code: <\/strong>If "APPLE" is coded as "BQQMF", the rule is: each letter is shifted forward by one position in the alphabet.<\/em>
      \nDecryption: <\/strong>To decrypt, we apply the reverse rule: shift each letter backward by one position.<\/em> So, "BQQMF" decrypts back to "APPLE".<\/p>\n

      Subtopics<\/u><\/strong><\/p>\n

      1. Concept of a Consistent Rule<\/strong><\/p>\n

      A pattern is only valid if it can be applied consistently across all given examples. The rule must work for every letter, number, or word in the set without exception.<\/p>\n

        \n
      • If the code for "CAT" is "ECV" and for "DOG" is "FQI", the rule must be the same for both (e.g., +2 shift for each letter).<\/li>\n
      • If one item does not follow the same rule, it is either incorrectly coded or the odd one out.<\/li>\n<\/ul>\n

        Key Points:<\/strong><\/p>\n

          \n
        • The rule can be based on position, order, mathematical operations, or a combination.<\/li>\n
        • Consistency is key to accurate decryption.<\/li>\n<\/ul>\n

          2. Identifying the Encryption Rule<\/strong><\/p>\n

          The first step in decryption is to hypothesize the encryption rule by comparing the original item to its code.<\/p>\n

          Steps to Identify the Rule:<\/strong><\/p>\n

            \n
          1. List<\/strong> the original items and their codes side-by-side.<\/li>\n
          2. Compare<\/strong> corresponding elements (first letter to first letter, etc.).<\/li>\n
          3. Look for Patterns:<\/strong> Check for constant shifts, mathematical relationships, reversals, or interleaving.<\/li>\n
          4. Test the Rule:<\/strong> Verify the hypothesized rule on all given examples to ensure it holds true.<\/li>\n<\/ol>\n

            Example 1 — Letter :<\/strong>
            \nOriginal: CAT → Code: ECV
            \nComparison: C→E (+2), A→C (+2), T→V (+2)
            \nRule:<\/strong> Each letter is moved forward by 2 positions in the alphabet.<\/p>\n

            Example 2 — Number Operation:<\/strong>
            \nOriginal: 4 → Code: 10
            \nPossible Rules: 4 × 2 + 2 = 10, or 4 + 6 = 10. Further examples are needed to confirm.<\/p>\n

            Pattern Recognition in Letter Codes<\/strong><\/p>\n

            Definition<\/u><\/strong><\/p>\n

            This involves decrypting codes where letters are transformed into other letters based on a specific, repeatable pattern. The pattern could be a fixed shift, a reverse order, a vowel-consonant modification, or a skipping sequence.<\/p>\n

            Importance of Letter Code Decryption<\/strong><\/p>\n

              \n
            • Improves familiarity with the alphabet and its positional values.<\/li>\n
            • Develops the ability to quickly see sequences and relationships.<\/li>\n
            • Directly applicable to a major subset of coding-decoding problems in exams.<\/li>\n<\/ul>\n

              Examples<\/strong><\/p>\n

                \n
              • Pattern 1 (Forward Shift):<\/strong> "LOVE" → "NQXG" (Rule: L+2=N, O+2=Q, V+2=X, E+2=G)<\/li>\n
              • Pattern 2 (Backward Shift):<\/strong> "ZOO" → "XMM" (Rule: Z-2=X, O-2=M, O-2=M)<\/li>\n
              • Pattern 3 (Reverse Order):<\/strong> "CODE" → "EDOC" (Rule: write the word backwards)<\/li>\n<\/ul>\n

                Subtopics<\/u><\/strong><\/p>\n

                1. Fixed Position Shifts<\/strong><\/p>\n

                The most common pattern, where each letter is shifted forward or backward by a fixed number of positions.<\/p>\n

                  \n
                • Forward Shift (Addition):<\/strong> A → C (+2), B → D (+2), etc.<\/li>\n
                • Backward Shift (Subtraction):<\/strong> D → B (-2), E → C (-2), etc.<\/li>\n<\/ul>\n

                  Quick Tip:<\/strong> If the shift goes past 'Z', it wraps around to 'A'. Similarly, going backwards past 'A' wraps around to 'Z'.<\/p>\n

                  Example Decryption:<\/strong>
                  \nIf the code is "GFK" and the rule is a +1 shift, the decryption is: G-1=F, F-1=E, K-1=J → "FEJ".<\/p>\n

                  2. Letter-Number Conversions (Positional Value)<\/strong><\/p>\n

                  Letters are converted to their positional values in the alphabet (A=1, B=2, …, Z=26) or vice-versa. Sometimes operations are performed on these numbers.<\/p>\n

                    \n
                  • Direct Conversion:<\/strong> "CAT" → "3 1 20"<\/li>\n
                  • Conversion with Operation:<\/strong> "CAT" → "4 2 21" (Rule: Position +1)<\/li>\n<\/ul>\n

                    Example Decryption:<\/strong>
                    \nCode: "5-16-12-9-20" → Positional values are 5,16,12,9,20.
                    \nConvert to letters: E, P, L, I, T → "EPLIT". Check for reversal? "EPLIT" reversed is "TILPE". Maybe the original was "TILPE"? Or perhaps the code itself is the direct letter conversion.<\/p>\n

                    3. Reverse Order and Jumbling<\/strong><\/p>\n

                    The sequence of letters is reversed or rearranged according to a fixed pattern.<\/p>\n

                      \n
                    • Full Reversal:<\/strong> "LOGIC" → "CIGOL"<\/li>\n
                    • Pairwise Reversal:<\/strong> "ABCD" → "BADC" (Swap positions 1&2, 3&4)<\/li>\n
                    • Fixed Position Jumble:<\/strong> "INPUT" → "PTUNI" (Rule: Position 1→3, 2→5, 3→1, 4→4, 5→2)<\/li>\n<\/ul>\n

                      Decryption Approach:<\/strong> To decrypt, you must identify the rearrangement pattern and apply the exact reverse.<\/p>\n

                      Pattern Recognition in Number Codes<\/strong><\/p>\n

                      Definition<\/u><\/strong><\/p>\n

                      Number code decryption involves finding the mathematical relationship between a given number and its code. This can include basic arithmetic operations, digit-based operations, or properties like squares and cubes.<\/p>\n

                      Importance of Number Code Decryption<\/strong><\/p>\n

                        \n
                      • Strengthens mathematical calculation and mental math skills.<\/li>\n
                      • Enhances the ability to see numerical patterns quickly.<\/li>\n
                      • Useful for data interpretation and puzzle-solving.<\/li>\n<\/ul>\n

                        Examples<\/strong><\/p>\n

                          \n
                        • Pattern 1 (Multiplication):<\/strong> 5 → 15 (Rule: 5 × 3 = 15)<\/li>\n
                        • Pattern 2 (Digit Sum):<\/strong> 123 → 6 (Rule: 1+2+3=6)<\/li>\n
                        • Pattern 3 (Square):<\/strong> 4 → 16 (Rule: 4² = 16)<\/li>\n<\/ul>\n

                          Subtopics<\/u><\/strong><\/p>\n

                          1. Basic Arithmetic Operations<\/strong><\/p>\n

                          The code is derived by performing a single arithmetic operation (+, -, ×, ÷) on the original number.<\/p>\n

                            \n
                          • Addition:<\/strong> Code = Number + k<\/li>\n
                          • Subtraction:<\/strong> Code = Number – k<\/li>\n
                          • Multiplication:<\/strong> Code = Number × k<\/li>\n
                          • Division:<\/strong> Code = Number ÷ k<\/li>\n<\/ul>\n

                            Example Decryption:<\/strong>
                            \nIf 7 → 21 and 4 → 12, the rule is likely ×3. So, for a code of 30, the original number would be 30 ÷ 3 = 10.<\/p>\n

                            2. Digit-based Operations<\/strong><\/p>\n

                            Operations are performed on the individual digits of the number.<\/p>\n

                              \n
                            • Digit Sum:<\/strong> Sum of all digits.<\/li>\n
                            • Digit Product:<\/strong> Product of all digits.<\/li>\n
                            • Digit Reverse:<\/strong> Number formed by writing digits in reverse order.<\/li>\n<\/ul>\n

                              Example Decryption:<\/strong>
                              \nCode: 18 (for the number 99). Check: 9+9=18 (Digit Sum). So the rule is "sum of digits".<\/p>\n

                              3. Properties and Relationships<\/strong><\/p>\n

                              The code is based on a mathematical property of the number, such as its square, cube, or whether it is prime or even.<\/p>\n

                                \n
                              • Perfect Square:<\/strong> Number 6 → Code 36 (6²)<\/li>\n
                              • Prime Number:<\/strong> Number 7 → Code "P" (indicating it's prime)<\/li>\n<\/ul>\n

                                Decryption Approach:<\/strong> Identify the property by testing common relationships against known examples.<\/p>\n

                                Mixed Alphanumeric Patterns<\/strong><\/p>\n

                                Definition<\/u><\/strong><\/p>\n

                                These are complex patterns that involve both letters and numbers in the code. The original item could be a word, a number, or an alphanumeric string, and the code is a mixture of letters and digits derived through a combined rule.<\/p>\n

                                Importance of Mixed Patterns<\/strong><\/p>\n

                                  \n
                                • Tests integrated logical reasoning skills.<\/li>\n
                                • Simulates real-world coding systems which are often alphanumeric.<\/li>\n
                                • Common in higher-difficulty exam questions.<\/li>\n<\/ul>\n

                                  Examples<\/strong><\/p>\n

                                    \n
                                  • Pattern 1 (Letter Position & Number):<\/strong> "CAT" → "C1T3" (Vowels are replaced by their position? A=1)<\/li>\n
                                  • Pattern 2 (Interleaving):<\/strong> "AB" and "12" → "A1B2"<\/li>\n<\/ul>\n

                                    Subtopics<\/u><\/strong><\/p>\n

                                    1. Letter-to-Number and Number-to-Letter<\/strong><\/p>\n

                                    Parts of the code are letters converted from numbers, and other parts are numbers converted from letters.<\/p>\n

                                      \n
                                    • Example:<\/strong> Original: "B5" → Code: "2E"
                                      \n\tPossible Rule: B's position is 2, 5's corresponding letter is E (the 5th letter). So, the rule is to swap the type.<\/li>\n<\/ul>\n

                                      Decryption:<\/strong> To decrypt "2E", swap back: 2→B, E→5 → "B5".<\/p>\n

                                      2. Positional Value with Operations<\/strong><\/p>\n

                                      The positional value of letters is calculated, and then an arithmetic operation is performed before presenting the final code.<\/p>\n

                                        \n
                                      • Example:<\/strong> "BAT" → "2-1-20" → Now multiply by 2? → "4-2-40". The code is "4240".<\/li>\n<\/ul>\n

                                        Decryption:<\/strong> Work backwards: "4240" could be split as 4, 2, 40. Reverse the operation (divide by 2) → 2, 1, 20. Convert to letters → "BAT".<\/p>\n

                                        Sequence and Series Based Decryption<\/strong><\/p>\n

                                        Definition<\/u><\/strong><\/p>\n

                                        This involves patterns where the code is derived from the position of the item in a sequence or series (like alphabetical order, numerical order, or a custom series).<\/p>\n

                                        Importance of Sequence-Based Decryption<\/strong><\/p>\n

                                          \n
                                        • Links coding-decoding to series completion skills.<\/li>\n
                                        • Requires understanding of different types of sequences (AP, GP, Alphabetical).<\/li>\n
                                        • Tests overall pattern recognition ability.<\/li>\n<\/ul>\n

                                          Examples<\/strong><\/p>\n

                                            \n
                                          • Pattern 1 (Alphabetical Series):<\/strong> Code represents the number of the letter in alphabetical order among a group.<\/li>\n
                                          • Pattern 2 (Fibonacci in Code):<\/strong> The code numbers follow a Fibonacci sequence.<\/li>\n<\/ul>\n

                                            Subtopics<\/u><\/strong><\/p>\n

                                            1. Alphabetical Order Value<\/strong><\/p>\n

                                            The code is based on the word's position if the words are arranged in alphabetical order.<\/p>\n

                                              \n
                                            • Example:<\/strong> Words: [Cat, Ant, Dog] in order: [Ant(1), Cat(2), Dog(3)].
                                              \n\tSo, "Cat" might be coded as "2".<\/li>\n<\/ul>\n

                                              Decryption:<\/strong> You need the sorted list to decrypt the code back to the original word.<\/p>\n

                                              2. Mathematical Series in Codes<\/strong><\/p>\n

                                              The codes themselves form a mathematical series like Arithmetic Progression (AP) or Geometric Progression (GP).<\/p>\n

                                                \n
                                              • Example:<\/strong> Codes for A, B, C, D are 2, 4, 6, 8. This is an AP with a common difference of 2.
                                                \n\tRule:<\/strong> Code = (Position of Letter) × 2.<\/li>\n<\/ul>\n

                                                Decryption:<\/strong> For a code of 10, the letter position is 10 ÷ 2 = 5, which is 'E'.<\/p>\n

                                                Example<\/u><\/strong>: –<\/strong><\/p>\n

                                                Examine the five coded words below. Exactly one code does NOT follow the same decryption rule<\/strong> as the other four. Identify the odd one out and provide a rigorous justification with three independent reasons<\/strong> from these domains: (A) Letter-based pattern consistency, (B) Numerical property of the code, (C) Semantic feasibility of the decrypted word<\/strong>.<\/p>\n

                                                Coded Words & Proposed Original Mapping (for analysis):<\/p>\n

                                                  \n
                                                1. RIVER<\/strong> is coded as IRREV<\/strong><\/li>\n
                                                2. MOUNTAIN<\/strong> is coded as NIATNUOM<\/strong><\/li>\n
                                                3. OCEAN<\/strong> is coded as NAECO<\/strong><\/li>\n
                                                4. DESERT<\/strong> is coded as TEREDS<\/strong><\/li>\n
                                                5. FOREST<\/strong> is coded as FOREZT<\/strong><\/li>\n<\/ol>\n

                                                  Question:<\/strong> Which one is the odd code out? Prove it by giving three independent reasons (letter pattern, numeric property, and semantic feasibility).<\/p>\n

                                                  Solution:<\/u><\/strong> –<\/strong><\/p>\n

                                                  (A) Letter-based Pattern Consistency (Reversal Test)<\/strong><\/p>\n

                                                  The first step is to hypothesize the encryption rule by comparing the original word to its code.<\/p>\n

                                                    \n
                                                  • RIVER <\/strong>→<\/strong> IRREV<\/strong>: This appears to be a reversal. "RIVER" reversed is "REVIR", not "IRREV". Let's check carefully. R(18)-I(9)-V(22)-E(5)-R(18). Code: I(9)-R(18)-R(18)-E(5)-V(22). It's not a perfect reversal. It looks like the first and last letters are swapped? R↔R? No change. Let's list all:<\/li>\n<\/ul>\n
                                                      \n
                                                    1. RIVER (Original: R,I,V,E,R) → Code: I,R,R,E,V. Pattern: Positions: 1→2, 2→1, 3→4, 4→5, 5→3? This is complex. Let's test a simpler rule: Full Reversal<\/strong>.<\/li>\n
                                                    2. MOUNTAIN → NIATNUOM. Check: "MOUNTAIN" reversed is "NIATNUOM". Yes! Perfect reversal.<\/li>\n
                                                    3. OCEAN → NAECO. Check: "OCEAN" reversed is "NAECO". Yes! Perfect reversal.<\/li>\n
                                                    4. DESERT → TEREDS. Check: "DESERT" reversed is "TRESED". The code is "TEREDS", which is close but not the same. T-R-E-S-E-D vs T-E-R-E-D-S. Not a perfect reversal.<\/li>\n
                                                    5. FOREST → FOREZT. Check: "FOREST" reversed is "TSEROF". The code "FOREZT" is completely different.<\/li>\n<\/ol>\n

                                                      This initial test is messy. Let's re-evaluate. Perhaps the rule is reverse the order of the letters<\/em>.<\/p>\n

                                                        \n
                                                      • Confirmed Reversals:\n
                                                          \n
                                                        • MOUNTAIN → NIATNUOM (Yes)<\/li>\n
                                                        • OCEAN → NAECO (Yes)<\/li>\n
                                                        • DESERT → TEREDS (Yes, "DESERT" reversed is "TEREDS". We were wrong earlier. D-E-S-E-R-T reversed is T-R-E-S-E-D? No, wait, spelling: D-E-S-E-R-T. Reversed: T-R-E-S-E-D. The code is T-E-R-E-D-S. This is not a reversal! There's a mismatch. Let's check the original document: "DESERT" is coded as "TEREDS". "DESERT" reversed should be "TRESED". The code "TEREDS" is not the same. So it's NOT a simple reversal.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

                                                          This inconsistency is the key. Let's define the rule based on the majority.<\/p>\n

                                                          From 1,2,3,4,5, it seems the intended rule is reversal of the letter order<\/strong>.<\/p>\n

                                                            \n
                                                          • 2. MOUNTAIN → NIATNUOM (Reversal, correct)<\/li>\n
                                                          • \n
                                                              \n
                                                            1. OCEAN → NAECO (Reversal, correct)<\/li>\n<\/ol>\n<\/li>\n
                                                            2. \n
                                                                \n
                                                              1. DESERT → TEREDS (Is this reversal? D-E-S-E-R-T -> T-R-E-S-E-D. The code is T-E-R-E-D-S. So R and E are swapped in the code? This is an error. Let's assume for the problem that DESERT->TEREDS is accepted<\/em> as a reversal, meaning they consider it correct spelling? Unlikely. Perhaps the rule is reverse the word<\/em>.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n

                                                                Let's list the reversal of each:<\/p>\n

                                                                  \n
                                                                1. RIVER -> REVIR (Code is IRREV, so No)<\/li>\n
                                                                2. MOUNTAIN -> NIATNUOM (Yes)<\/li>\n
                                                                3. OCEAN -> NAECO (Yes)<\/li>\n
                                                                4. DESERT -> TRESED (Code is TEREDS, so No)<\/li>\n
                                                                5. FOREST -> TSEROF (Code is FOREZT, so No)<\/li>\n<\/ol>\n

                                                                  Only 2 and 3 follow the reversal rule perfectly. This is problematic. Perhaps the rule is not reversal. Let's check another pattern: Maybe the code is the original word sorted alphabetically?<\/p>\n

                                                                    \n
                                                                  • RIVER sorted: E,I,R,R,V -> EIRRV. Code is IRREV. No.
                                                                    \n\tThis is taking too long. Let's assume the intended common rule for the majority is reversal<\/strong>, and the ones that don't match are odd.<\/li>\n<\/ul>\n

                                                                    Conclusion (A):<\/strong> If the decryption rule is "reverse the string to get the original word", then:<\/p>\n

                                                                      \n
                                                                    • Code NIATNUOM decrypts to MOUNTAIN (Valid word).<\/li>\n
                                                                    • Code NAECO decrypts to OCEAN (Valid word).<\/li>\n
                                                                    • Code TEREDS decrypts to TRESED (Invalid word, not "DESERT"). So #4 fails.<\/li>\n
                                                                    • Code IRREV decrypts to VIRRE (Invalid word, not "RIVER"). So #1 fails.<\/li>\n
                                                                    • Code FOREZT decrypts to TZEROF (Invalid word, not "FOREST"). So #5 fails.<\/li>\n<\/ul>\n

                                                                      This doesn't give a single odd one out. Let's look for a different pattern. Notice in #5 FOREST -> FOREZT. The first four letters are the same "FORE", but the last two letters "ST" become "ZT". This looks like a letter shift for only part of the word, breaking the pattern. The others seem to be reversals. Let's check #1: RIVER->IRREV. If reversed, it should be REVIR. The code IRREV is an anagram. Similarly, #4 DESERT->TEREDS is an anagram of the reverse? TRESED vs TEREDS. They are anagrams.<\/p>\n

                                                                      A more consistent observation: Items 1,2,3,4 are all anagrams of their reversed string. Item 5 is not.<\/p>\n

                                                                        \n
                                                                      • RIVER reversed=REVIR, anagram? R,E,V,I,R vs I,R,R,E,V -> same letters? Yes, both have R,R,E,V,I.<\/li>\n
                                                                      • MOUNTAIN reversed=NIATNUOM, anagram? Yes.<\/li>\n
                                                                      • OCEAN reversed=NAECO, anagram? Yes.<\/li>\n
                                                                      • DESERT reversed=TRESED, anagram of TEREDS? T,R,E,S,E,D vs T,E,R,E,D,S -> same letters? Yes, T,R,E,S,E,D vs T,E,R,E,D,S -> both have 2xE, 1xT,1xR,1xS,1xD. Yes.<\/li>\n
                                                                      • FOREST reversed=TSEROF, anagram of FOREZT? T,S,E,R,O,F vs F,O,R,E,Z,T -> Letters: F,O,R,E,S,T vs F,O,R,E,Z,T. The code has Z instead of S. So it is NOT an anagram. The letter set is different.<\/li>\n<\/ul>\n

                                                                        Thus, for Test (A):<\/strong> FOREST (5) is the odd one out because it is the only one whose code is not an anagram of the original word's reversal. The codes for 1,2,3,4 are all anagrams of the reversed original word.<\/p>\n

                                                                        (B) Numerical Property of the Code (Sum of Letter Positions)<\/strong><\/p>\n

                                                                        Convert each code word into the sum of the positional values of its letters (A=1, B=2… Z=26).<\/p>\n

                                                                          \n
                                                                        1. IRREV: I=9, R=18, R=18, E=5, V=22 → Sum = 9+18+18+5+22 = 72<\/strong><\/li>\n
                                                                        2. NIATNUOM: N=14,I=9,A=1,T=20,N=14,U=21,O=15,M=13 → Sum = 14+9+1+20+14+21+15+13 = 107<\/strong><\/li>\n
                                                                        3. NAECO: N=14,A=1,E=5,C=3,O=15 → Sum = 14+1+5+3+15 = 38<\/strong><\/li>\n
                                                                        4. TEREDS: T=20,E=5,R=18,E=5,D=4,S=19 → Sum = 20+5+18+5+4+19 = 71<\/strong><\/li>\n
                                                                        5. FOREZT: F=6,O=15,R=18,E=5,Z=26,T=20 → Sum = 6+15+18+5+26+20 = 90<\/strong><\/li>\n<\/ol>\n

                                                                          Now, let's check the numerical properties of these sums (Primality, Even\/Odd, Perfect Square):<\/p>\n

                                                                            \n
                                                                          • 72: Even, Composite, Perfect Square? (8.48^2, no), 72 is not a perfect square.<\/li>\n
                                                                          • 107: Odd, Prime<\/strong>.<\/li>\n
                                                                          • 38: Even, Composite.<\/li>\n
                                                                          • 71: Odd, Prime<\/strong>.<\/li>\n
                                                                          • 90: Even, Composite.<\/li>\n<\/ul>\n

                                                                            Conclusion (B):<\/strong> The sums are 72, 107, 38, 71, 90. Two of them (107 and 71) are prime numbers. The others are composite. Item 5 (FOREZT) has a sum of 90, which is composite. This doesn't single it out. However, 90 is a multiple of 10 (9×10) and is a Harshad number (90\/9=10). But let's find a unique property. Notice that 90 is the only sum that is divisible by 10. 90 ÷ 10 = 9. None of the others are divisible by 10 (72\/10=7.2, 107\/10=10.7, etc.). This is a clear, unique numeric property for code 5.<\/p>\n

                                                                            Thus, for Test (B):<\/strong> The code FOREZT has a letter-position sum (90) that is divisible by 10. This is not true for any of the other four codes.<\/p>\n

                                                                            (C) Semantic Feasibility of the Decrypted Word<\/strong><\/p>\n

                                                                            Assume the decryption rule is "reverse the code to get the original word". Let's see what words we get and if they are semantically valid (real English words related to nature\/geography).<\/p>\n

                                                                              \n
                                                                            1. Code: IRREV → Reverse: VIRRE (Not a valid English word).<\/li>\n
                                                                            2. Code: NIATNUOM → Reverse: MOUNTAIN (Valid word, geographical feature).<\/li>\n
                                                                            3. Code: NAECO → Reverse: OCEAN (Valid word, geographical feature).<\/li>\n
                                                                            4. Code: TEREDS → Reverse: STRET (Not a valid English word). Or is it? "STRET" isn't standard. "DESERT" reversed is "TRESED", not "TEREDS". So decrypting "TEREDS" by reversal gives "SERET"?
                                                                              \n\tLet's be precise: T-E-R-E-D-S reversed is S-D-E-R-E-T -> "SDERET" (Invalid).
                                                                              \n\tBut if we consider the intended original is DESERT, then the code should be TRESED. Since it's not, this is a flaw.<\/li>\n
                                                                            5. Code: FOREZT → Reverse: TZEROF (Not a valid English word).<\/li>\n<\/ol>\n

                                                                              This is confusing. Perhaps the rule is not reversal. Maybe the code is the original word. But that doesn't make sense for a coding problem.<\/p>\n

                                                                              Let's use the pattern from (A). The common rule for 1,2,3,4 is that the code is an anagram of the reversed original word. So to decrypt, you rearrange the code's letters to form the original word.<\/p>\n

                                                                                \n
                                                                              • Code IRREV can be rearranged to RIVER. (Valid)<\/li>\n
                                                                              • Code NIATNUOM can be rearranged to MOUNTAIN. (Valid)<\/li>\n
                                                                              • Code NAECO can be rearranged to OCEAN. (Valid)<\/li>\n
                                                                              • Code TEREDS can be rearranged to DESERT. (Valid)<\/li>\n
                                                                              • Code FOREZT can be rearranged to… F,O,R,E,Z,T. There is no common English word for these letters. "FORZET" isn't a word. "FORTEZ" isn't standard. It cannot form "FOREST" because it has a Z instead of an S.<\/li>\n<\/ul>\n

                                                                                Conclusion (C):<\/strong> Therefore, semantically, the first four codes can be decrypted (via anagramming) back to valid, meaningful geographical words (RIVER, MOUNTAIN, OCEAN, DESERT). The fifth code, FOREZT, cannot be decrypted into a valid English word using the same anagramming logic because it contains a 'Z' that does not fit the word "FOREST". It is semantically invalid in this context.<\/p>\n

                                                                                Final Ruling:<\/strong><\/p>\n

                                                                                Because these three distinguishing tests are independent<\/strong> (Letter pattern consistency, Unique numeric property, and Semantic feasibility), FOREZT (Code for FOREST)<\/strong> is definitively the odd one out.<\/p>\n

                                                                                 <\/p>\n","protected":false},"excerpt":{"rendered":"

                                                                                Unit: Coding & Decoding Chapter: Decryption of Patterns Reference: – Introduction to Decryption, Pattern Recognition in Letter Codes, Pattern Recognition in Number Codes, Mixed Alphanumeric Patterns, Positional Value Decryption, Mathematical Operation Decryption, Sequence and Series Based Decryption After studying this chapter, you should be able to understand: Introduction to Classification The fundamental concept of decryption […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[570],"tags":[],"class_list":["post-9164","post","type-post","status-publish","format-standard","hentry","category-math-sci-olympiad"],"_links":{"self":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/9164","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/comments?post=9164"}],"version-history":[{"count":0,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/9164\/revisions"}],"wp:attachment":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/media?parent=9164"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/categories?post=9164"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/tags?post=9164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}