Understanding the Letter Coding Pattern

This question involves a letter coding pattern where each letter in the word 'PAINTER' is assigned a numerical digit. We need to decipher this pattern and apply it to find the code for the word 'POEM'.

Analyzing the Given Code: PAINTER is 7195259

Let's look at the letters in PAINTER and their corresponding digits:

• P is coded as 7
• A is coded as 1
• I is coded as 9
• N is coded as 5
• T is coded as 2
• E is coded as 5
• R is coded as 9

Some digits repeat for different letters (e.g., 5 for N and E, 9 for I and R), which suggests the code is not a simple 1-to-1 alphabetical mapping.

Discovering the Letter Coding Rule

Let's consider the alphabetical position of each letter and see if there's a relationship with the assigned digit.

• P is the 16th letter
• A is the 1st letter
• I is the 9th letter
• N is the 14th letter
• T is the 20th letter
• E is the 5th letter
• R is the 18th letter

Let's examine the relationship between the alphabetical position and the given code:

• P (16th) → 7
• A (1st) → 1
• I (9th) → 9
• N (14th) → 5
• T (20th) → 2
• E (5th) → 5
• R (18th) → 9

Observe that for letters with a single-digit position (A, I, E), the code is the position itself. For letters with a two-digit position (P, N, T, R), let's try summing the digits of their position:

• P (16th): \(1 + 6 = 7\). This matches the code 7.
• N (14th): \(1 + 4 = 5\). This matches the code 5.
• T (20th): \(2 + 0 = 2\). This matches the code 2.
• R (18th): \(1 + 8 = 9\). This matches the code 9.

The rule is: The code for a letter is the sum of the digits of its alphabetical position. If the position is a single digit, the code is the position itself (which is equivalent to the sum of digits if we consider the first digit as 0, e.g., A is 01st, 0+1=1, or simply the digit itself).

Applying the Rule to Code POEM

Now we apply the same rule to the letters in the word POEM:

• P: The 16th letter. Sum of digits is \(1 + 6 = 7\). Code for P is 7.
• O: The 15th letter. Sum of digits is \(1 + 5 = 6\). Code for O is 6.
• E: The 5th letter. Position is a single digit. Code for E is 5.
• M: The 13th letter. Sum of digits is \(1 + 3 = 4\). Code for M is 4.

Combining the codes for P, O, E, and M, we get 7654.

Conclusion: The Code for POEM

Based on the established coding pattern, the word POEM is written as 7654.

Let's compare this result with the given options:

• 1651351
• 7654
• 7556
• 20181914

Our calculated code 7654 matches the second option.

Revision Table: Coding Rule Summary

Additional Information: Types of Letter Coding

Letter coding questions are common in reasoning tests and can follow various patterns. Some typical types include:

• Alphabetical Position: Letters are coded by their direct position in the alphabet (A=1, B=2, etc.) or reverse position (A=26, B=25, etc.).
• Letter Shifting: Each letter is shifted a fixed number of positions forward or backward in the alphabet (e.g., A becomes C, B becomes D - shifting by +2).
• Opposite Letters: Letters are coded by their opposite letter in the alphabet (A opposite Z, B opposite Y, etc.).
• Consonant/Vowel Coding: Vowels might be coded differently from consonants, or follow a separate sequence.
• Arbitrary Assignment: Letters are assigned codes based on a specific table provided or implied by the examples, as seen in this question (though here it was a derived rule, not completely arbitrary).
• Mixed Patterns: Combinations of the above patterns can be used.

Solving coding-decoding problems requires careful observation, pattern identification, and systematic application of the found rule.