Understanding Coding Decoding: Finding the Code for CRAPE

This question is a classic example of a direct letter coding problem, where each letter in the given words corresponds to a specific digit. We are given the codes for 'ROPE' and 'CHAIR', and we need to find the code for 'CRAPE' using the same logic.

Step-by-Step Analysis of Given Codes

Let's break down the given information to find the unique code assigned to each letter:

• ROPE is coded as 6821
  • R corresponds to 6
  • O corresponds to 8
  • P corresponds to 2
  • E corresponds to 1
• CHAIR is coded as 73456
  • C corresponds to 7
  • H corresponds to 3
  • A corresponds to 4
  • I corresponds to 5
  • R corresponds to 6

Consolidating the Letter-Digit Mapping

From the analysis above, we can create a mapping of each letter present in the words to its corresponding digit:

Notice that the letter 'R' appears in both 'ROPE' and 'CHAIR', and its code is consistently '6', confirming our direct coding logic.

Coding the Word 'CRAPE'

Now, we will use the established mapping to find the code for the word 'CRAPE'. We take each letter of 'CRAPE' and substitute its corresponding digit code:

• C maps to 7
• R maps to 6
• A maps to 4
• P maps to 2
• E maps to 1

Putting the digits together in the order they appear in 'CRAPE', we get the code:

\( \text{C} \rightarrow 7 \)
\( \text{R} \rightarrow 6 \)
\( \text{A} \rightarrow 4 \)
\( \text{P} \rightarrow 2 \)
\( \text{E} \rightarrow 1 \)

So, the code for 'CRAPE' is 76421.

Revision Table: Key Coding Details

Additional Information: Types of Coding Decoding

Coding-decoding is a common topic in logical reasoning. Problems can appear in various forms, not just direct letter-to-digit mapping. Some other types include:

• Letter Coding: Letters are substituted with other letters based on a pattern (e.g., shifting letters forward or backward in the alphabet).
• Number Coding: Words are coded into numbers based on the letter's position in the alphabet, sum of positions, or other numerical relationships.
• Symbol Coding: Letters or words are coded using symbols.
• Mixed Coding: A combination of letters, numbers, and symbols are used.
• Chinese Coding (or Common Word Coding): A set of sentences is given with their coded versions, and you find the code for specific words by identifying common words and codes across sentences.

Understanding the basic pattern, like direct mapping demonstrated in this 'CRAPE' example, is crucial for solving various coding decoding problems in exams.