Coding Decoding Pattern Analysis

This is a classic coding-decoding question where we need to identify the specific pattern or rule used to transform one word into another. Once the pattern is found, we apply it to the target word to find its coded form. We are given two examples of coding: MELON is coded as TCSKU, and CHAMP is coded as JFHIW. We need to find the code for FAMISH.

Identifying the Coding Rule

Let's analyze the transformation of each letter based on its position in the word. We can assign a numerical value to each letter of the alphabet (A=1, B=2, ..., Z=26).

Analyzing MELON to TCSKU:

• The 1st letter M (13) becomes T (20). The difference is $20 - 13 = 7$. So, Position 1: $+7$.
• The 2nd letter E (5) becomes C (3). The difference is $3 - 5 = -2$. So, Position 2: $-2$.
• The 3rd letter L (12) becomes S (19). The difference is $19 - 12 = 7$. So, Position 3: $+7$.
• The 4th letter O (15) becomes K (11). The difference is $11 - 15 = -4$. So, Position 4: $-4$.
• The 5th letter N (14) becomes U (21). The difference is $21 - 14 = 7$. So, Position 5: $+7$.

The pattern observed for the first 5 letters is: $+7, -2, +7, -4, +7$.

Analyzing CHAMP to JFHIW:

Let's verify this pattern with the second example.

• The 1st letter C (3) becomes J (10). The difference is $10 - 3 = 7$. Position 1: $+7$.
• The 2nd letter H (8) becomes F (6). The difference is $6 - 8 = -2$. Position 2: $-2$.
• The 3rd letter A (1) becomes H (8). The difference is $8 - 1 = 7$. Position 3: $+7$.
• The 4th letter M (13) becomes I (9). The difference is $9 - 13 = -4$. Position 4: $-4$.
• The 5th letter P (16) becomes W (23). The difference is $23 - 16 = 7$. Position 5: $+7$.

The pattern $+7, -2, +7, -4, +7$ is consistently applied to the first five letters in both examples. This suggests the pattern depends on the position of the letter in the word.

Applying the Rule to FAMISH

Now we apply this position-based pattern to the word FAMISH, which has 6 letters. We will apply the pattern $+7, -2, +7, -4, +7$ to the first five letters and determine the rule for the 6th letter based on the provided options. Let's calculate the transformation for each letter of FAMISH:

• F (1st letter, position 6): Apply $+7$. $\text{6} + \text{7} = \text{13}$. The 13th letter is M.
• A (2nd letter, position 1): Apply $-2$. $\text{1} - \text{2} = \text{-1}$. When the result is negative, we wrap around the alphabet from Z (26). So, $\text{1} - \text{2} \equiv \text{-1} \pmod{\text{26}}$. This is equivalent to $\text{26} + \text{-1} = \text{25}$. The 25th letter is Y.
• M (3rd letter, position 13): Apply $+7$. $\text{13} + \text{7} = \text{20}$. The 20th letter is T.
• I (4th letter, position 9): Apply $-4$. $\text{9} - \text{4} = \text{5}$. The 5th letter is E.
• S (5th letter, position 19): Apply $+7$. $\text{19} + \text{7} = \text{26}$. The 26th letter is Z.
• H (6th letter, position 8): We need to find the pattern for the 6th position. Let's look at the options provided. The first option is MYTEZB. The first five letters match our calculations (MYTEZ). The 6th letter in this option is B. Let's see what transformation is needed to get from H (8) to B (2). $\text{2} - \text{8} = \text{-6}$. So, the rule for the 6th position appears to be $-6$. Let's assume the pattern continues with alternating signs and increasing subtrahends for subtraction terms: $+7, -2, +7, -4, +7, -6, +7, -8, \dots$ Applying $-6$ to H: $\text{8} - \text{6} = \text{2}$. The 2nd letter is B.

Combining the letters, the coded word for FAMISH is MYTEZB.

This matches the first option.

Coding Decoding Revision Table

The table summarizes how the pattern is derived and applied, showing the letter positions and the resulting transformations.

Additional Information on Letter Coding

Letter coding is a common type of coding-decoding question in reasoning sections of competitive exams. It involves replacing each letter of a word with another letter or a symbol based on a specific rule or pattern. Common patterns include:

• Adding or subtracting a fixed number to the letter's position (e.g., each letter shifted by +3).
• Adding or subtracting a varying number based on the letter's position (as seen in this problem).
• Reversing the order of letters or blocks of letters.
• Substituting letters based on their position in the alphabet or a predefined code table.
• Vowel/consonant specific rules.
• Opposite letter rules (A is opposite Z, B is opposite Y, etc., based on A=1, Z=26 and A+Z=27, B+Y=27).

To solve letter coding problems, it's helpful to know the alphabetical position of each letter and practice identifying different types of patterns quickly.