Understanding the Coding Pattern

This question asks us to find a numerical code for the word DEMON based on the given codes for BUN and MICE. This is a classic letter coding or word coding problem where we need to identify the rule or pattern used to convert a word into a number.

Analyzing Given Examples: BUN and MICE

We are given two examples:

• BUN is coded as 18.
• MICE is coded as 32.

Let's analyze these examples to find a pattern. A common approach in such coding puzzles is to look at the alphabetical positions of the letters (A=1, B=2, ..., Z=26) or the number of letters in the word.

Analyzing BUN:

• Letters: B, U, N
• Number of letters (N) = 3
• Alphabetical positions: B=2, U=21, N=14
• Sum of alphabetical positions = \(2 + 21 + 14 = 37\). The given code is 18.

Analyzing MICE:

• Letters: M, I, C, E
• Number of letters (N) = 4
• Alphabetical positions: M=13, I=9, C=3, E=5
• Sum of alphabetical positions = \(13 + 9 + 3 + 5 = 30\). The given code is 32.

The sum of alphabetical positions does not directly match the codes (37 vs 18, and 30 vs 32). Let's look for another pattern, possibly involving the number of letters.

Discovering the Rule

Let's examine the relationship between the number of letters (N) and the given code for each word:

We observe a sequence in the 'Code / N' column: 6 and 8. This sequence increases by 2 when the number of letters (N) increases by 1 (from 3 to 4). This suggests a pattern where 'Code / N' is related to N itself.

Let's check if the pattern is \( \frac{\text{Code}}{\text{N}} = k \times \text{N} \) for some constant k. For BUN (N=3): \( \frac{18}{3} = 6 \). If \( \frac{\text{Code}}{\text{N}} = k \times \text{N} \), then \( 6 = k \times 3 \implies k = \frac{6}{3} = 2 \). For MICE (N=4): \( \frac{32}{4} = 8 \). If \( \frac{\text{Code}}{\text{N}} = k \times \text{N} \) with \(k=2\), then \( 8 = 2 \times 4 = 8 \). This matches!

The consistent pattern we found is \( \frac{\text{Code}}{\text{N}} = 2 \times \text{N} \). This can be rewritten as \( \text{Code} = \text{N} \times (2 \times \text{N}) = 2 \times \text{N}^2 \).

Let's verify this rule with the given examples:

• For BUN: N=3. Code \( = 2 \times 3^2 = 2 \times 9 = 18 \). This matches the given code for BUN.
• For MICE: N=4. Code \( = 2 \times 4^2 = 2 \times 16 = 32 \). This matches the given code for MICE.

The rule appears to be: The code for a word is 2 times the square of the number of letters in the word.

Calculating the Code for DEMON

Now, we apply this rule to find the code for the word DEMON.

First, count the number of letters in DEMON.

• Letters: D, E, M, O, N
• Number of letters (N) = 5

Using the discovered rule \( \text{Code} = 2 \times \text{N}^2 \):

Code for DEMON \( = 2 \times 5^2 \)

\( = 2 \times (5 \times 5) \)

\( = 2 \times 25 \)

\( = 50 \)

Final Answer

Based on the pattern derived from BUN and MICE, the code for DEMON is 50.

Revision Table: Coding Puzzle Summary

Additional Information: Letter Coding Concepts

Letter coding and decoding are common types of questions in reasoning and aptitude tests. They assess your ability to identify patterns and apply rules. While this problem used a rule based on the number of letters, other problems might involve:

• Positional Values: Using the sequence number of letters in the alphabet (A=1, B=2, etc., or Z=1, Y=2, etc.). The code might be the sum, product, or other function of these values.
• Letter Shifting: Replacing each letter with a letter a certain number of positions away in the alphabet (e.g., A becomes C, B becomes D - a shift of +2).
• Substitution: Assigning a specific code (letter, number, or symbol) to each letter in the original word.
• Reverse Order: Reversing the letters of the word before applying another rule.

Practice with various types of letter coding puzzles helps in quickly recognizing the underlying logic during exams.