Decoding the Code Language: HUT, MAT, and BIB

This problem involves understanding a simple code language where words are represented by numbers. We are given two examples to figure out the rule, and then we apply that rule to a third word.

Understanding Positional Values of Letters

In many coding and decoding problems, letters are assigned numerical values based on their position in the English alphabet. A is typically 1, B is 2, C is 3, and so on, up to Z which is 26. Let's list the values for the letters in our given words:

• H: 8
• U: 21
• T: 20
• M: 13
• A: 1
• B: 2
• I: 9

Analysing the Given Codes: HUT and MAT

Let's see if the code is related to the sum of the positional values of the letters in each word.

For 'HUT':

The letters are H, U, T. Their positional values are 8, 21, and 20.

Sum of positional values for HUT = \(\text{Value(H)} + \text{Value(U)} + \text{Value(T)}\)

Sum = \(8 + 21 + 20 = 49\)

The given code for HUT is 55.

Difference = Given Code - Sum of values = \(55 - 49 = 6\)

For 'MAT':

The letters are M, A, T. Their positional values are 13, 1, and 20.

Sum of positional values for MAT = \(\text{Value(M)} + \text{Value(A)} + \text{Value(T)}\)

Sum = \(13 + 1 + 20 = 34\)

The given code for MAT is 40.

Difference = Given Code - Sum of values = \(40 - 34 = 6\)

In both cases, the given code is 6 more than the sum of the positional values of the letters. This suggests the rule is: Code = Sum of positional values + 6.

Applying the Rule to 'BIB'

Now let's apply this rule to find the code for the word 'BIB'.

The letters are B, I, B. Their positional values are 2, 9, and 2.

Sum of positional values for BIB = \(\text{Value(B)} + \text{Value(I)} + \text{Value(B)}\)

Sum = \(2 + 9 + 2 = 13\)

Using the rule (Code = Sum of values + 6):

Code for BIB = \(13 + 6 = 19\)

Therefore, 'BIB' will be coded as '19' in this language.

Summary of Calculations

The calculated code for BIB is 19.

Revision Table: Code Language Analysis

Reviewing the steps taken to solve the coding problem:

• Identify the given words and their codes.
• Determine the positional values of the letters in each word.
• Calculate the sum of positional values for the example words (HUT and MAT).
• Compare the sum of values with the given codes to find the pattern or rule (adding 6 in this case).
• Apply the identified rule to the target word (BIB) to find its code.

Additional Information: Types of Coding Decoding

Coding and decoding questions are common in reasoning sections of competitive exams. They test your ability to find patterns. Some common types include:

• Letter Coding: Letters are replaced by other letters based on a rule (e.g., shifting letters, reversing order).
• Number Coding: Words or letters are represented by numbers, often based on positional values, sum of values, number of letters, or other numerical operations.
• Symbol Coding: Letters or words are replaced by symbols.
• Mixed Coding: A combination of word, number, and symbol codes.

This problem is an example of Number Coding based on positional values with an added constant.