Coding - Decoding | Mathematics Olympiad Class 4 PDF Download

Meaning

Types of Coding-Decoding

1. Letter Coding: Involves replacing letters of the alphabet with other letters based on a specific rule or pattern.
Rule: Move each letter one step forward in the alphabet.
A → B,  B → C,  C → D, …,  Y → Z,  Z → A
Example: “CAT” → ?

So, CAT → D B U

If A is coded as B, B is coded as C, and so on, then CAT will be coded as DBU.

2. Number Coding: Involves replacing letters with corresponding numbers based on a given rule.
Rule: Replace each letter by its position in the alphabet (A=1, B=2, …, Z=26).

Example: CAT → ?

• C → 3
• A → 1
• T → 20

So, CAT → 3–1–20

So, If A is coded as 1, B as 2, C as 3, and so on, then CAT will be coded as 3-1-20.

3. Mixed Coding: Combines both letter and number coding in a single problem.

• Example: If A is coded as B, B is coded as 2, C is coded as D, and so on, then CAT will be coded as DB3.

4. Substitution Coding: Involves replacing a group of letters with another group of letters based on a given rule.
Rule: Apply a fixed letter-to-letter substitution. Here we’ll use a +1 shift again:

Example 1: apple → ?

• a → b
• p → q
• p → q
• l → m
• e → f

Result: b q q m f

Example 2: banana → ?

• b → c
• a → b
• n → o
• a → b
• n → o
• a → b

Result: c b o b o b

So, If 'apple' is coded as 'bqqmf,' then 'banana' will be coded as 'cboanb.'

Strategies for Solving Coding-Decoding Problems

Identify the Pattern:

• Analyze the given code to understand the relationship between the original message and its coded form.
• Look for recurring patterns, such as alphabetical order, numerical sequence, or reverse order.

Use Trial and Error:

• If the pattern is not immediately apparent, try applying different rules systematically to decode the message.

Look for Clues:

• Pay attention to any hints or clues provided in the problem statement that could help decipher the code.

Check for Consistency:

• Ensure that the same rule is applied consistently throughout the coding or decoding process.

Solved Examples

(i) If 'PENCIL' is coded as 'QFODJM,' how is 'PAPER' coded?
Sol: Shift each letter one step forward (A→B, B→C, …).
To code PAPER:

• P → Q
• A → B
• P → Q
• E → F
• R → S

Answer: PAPER → QBQFS

(ii) If 'RIVER' is coded as '12341' and 'CLOUD' is coded as '56789,' how is 'CIDER' coded?

Sol: Each letter is replaced by a specific digit (learned from the two examples):

• From RIVER → 1 2 3 4 1 we get R=1, I=2, V=3, E=4
• From CLOUD → 5 6 7 8 9 we get C=5, L=6, O=7, U=8, D=9

To code CIDER:

• C → 5
• I → 2
• D → 9
• E → 4
• R → 1

Answer: CIDER → 52941

(iii) If 'HOUSE' is coded as 'GNTRD,' what is the code for 'BRICK'?

Sol: Rule: Shift each letter one step backward (A←B, B←C, …).
To code BRICK:

• B → A
• R → Q
• I → H
• C → B
• K → J

Answer: BRICK → AQHBJ