Decoding the Letter Coding Pattern for LARVAE

The problem presents a coding language where the word LARVAE is coded as 15-1-9-5-1-2. We need to decipher this pattern and apply it to find the code for the word INSECT.

Step 1: Alphabetical Positions Analysis

First, let's list the standard alphabetical positions for each letter in the example word LARVAE:

• L is the 12th letter.
• A is the 1st letter.
• R is the 18th letter.
• V is the 22nd letter.
• A is the 1st letter.
• E is the 5th letter.

Step 2: Identifying the Coding Logic

Comparing the standard positions (12, 1, 18, 22, 1, 5) with the given code (15-1-9-5-1-2), we notice discrepancies. Let's explore different coding schemes, such as using positions from the end of the alphabet (reverse positions) and special handling for vowels.

The reverse alphabetical position is calculated as $ 27 - (\text{Standard Position}) $. Let's compute this for LARVAE:

• L (12): Reverse position is $ 27 - 12 = 15 $. Code given is 15. (Match)
• A (1): Reverse position is $ 27 - 1 = 26 $. Code given is 1. (Mismatch)
• R (18): Reverse position is $ 27 - 18 = 9 $. Code given is 9. (Match)
• V (22): Reverse position is $ 27 - 22 = 5 $. Code given is 5. (Match)
• A (1): Reverse position is $ 27 - 1 = 26 $. Code given is 1. (Mismatch)
• E (5): Reverse position is $ 27 - 5 = 22 $. Code given is 2. (Mismatch)

We see that the reverse position rule applies correctly only to the consonants (L, R, V).

Step 3: Determining the Vowel Coding Rule

Let's focus on the vowels in LARVAE: A, A, E. Their codes are 1, 1, 2 respectively.

The standard positions are A=1, E=5. The sequence of vowels is A, E, I, O, U.

It appears the code for vowels depends on their sequence number:

• A is the 1st vowel, and its code is 1.
• E is the 2nd vowel, and its code is 2.

This rule fits the given code for LARVAE perfectly.

Step 4: Applying the Pattern to INSECT

The coding rule is confirmed as:

• Consonants: Coded by their reverse alphabetical position ($ 27 - \text{Standard Position} $).
• Vowels: Coded by their sequence number (A=1, E=2, I=3, O=4, U=5).

Now, let's apply this rule to the word INSECT:

• I (Vowel): I is the 3rd vowel. Code = 3.
• N (Consonant): Standard position is 14. Reverse position = $ 27 - 14 = 13 $. Code = 13.
• S (Consonant): Standard position is 19. Reverse position = $ 27 - 19 = 8 $. Code = 8.
• E (Vowel): E is the 2nd vowel. Code = 2.
• C (Consonant): Standard position is 3. Reverse position = $ 27 - 3 = 24 $. Code = 24.
• T (Consonant): Standard position is 20. Reverse position = $ 27 - 20 = 7 $. Code = 7.

Step 5: Constructing the Code for INSECT

Combining the codes for each letter of INSECT gives us: 3-13-8-2-24-7.

Step 6: Selecting the Correct Option

Let's compare this result with the provided options:

Our calculated code, 3-13-8-2-24-7, matches exactly with Option 4.