Understanding Letter Position Coding

This question presents a coding-decoding puzzle where words are transformed into numerical sequences. We need to identify the pattern by analyzing the given examples and then apply it to find the code for the target word.

Analyzing the Given Examples

Let's examine how 'LEATHER' and 'ABSCOND' are coded.

Example 1: LEATHER is coded as 1251208518

Let's look at the alphabetical position of each letter in LEATHER:

• L is the $\text{12}^{\text{th}}$ letter.
• E is the $\text{5}^{\text{th}}$ letter.
• A is the $\text{1}^{\text{st}}$ letter.
• T is the $\text{20}^{\text{th}}$ letter.
• H is the $\text{8}^{\text{th}}$ letter.
• E is the $\text{5}^{\text{th}}$ letter.
• R is the $\text{18}^{\text{th}}$ letter.

If we concatenate these position numbers directly, we get 12 followed by 5, then 1, then 20, then 8, then 5, and finally 18. This sequence is 1251208518, which exactly matches the given code for LEATHER.

Example 2: ABSCOND is coded as 1219315144

Let's look at the alphabetical position of each letter in ABSCOND:

• A is the $\text{1}^{\text{st}}$ letter.
• B is the $\text{2}^{\text{nd}}$ letter.
• S is the $\text{19}^{\text{th}}$ letter.
• C is the $\text{3}^{\text{rd}}$ letter.
• O is the $\text{15}^{\text{th}}$ letter.
• N is the $\text{14}^{\text{th}}$ letter.
• D is the $\text{4}^{\text{th}}$ letter.

Now, let's concatenate these position numbers: 1, 2, 19, 3, 15, 14, 4. When concatenated, this gives 1219315144, which perfectly matches the given code for ABSCOND.

Identifying the Coding Logic

From the two examples, the logic of the coding language is clear. Each letter in the word is replaced by its numerical position in the English alphabet (A=1, B=2, ..., Z=26). These numerical positions are then written one after another without any separator to form the complete code for the word.

Applying the Logic to DESTROY

Now, let's apply this letter position coding logic to the word DESTROY to find its code.

• D is the $\text{4}^{\text{th}}$ letter of the alphabet. Code part: 4
• E is the $\text{5}^{\text{th}}$ letter of the alphabet. Code part: 5
• S is the $\text{19}^{\text{th}}$ letter of the alphabet. Code part: 19
• T is the $\text{20}^{\text{th}}$ letter of the alphabet. Code part: 20
• R is the $\text{18}^{\text{th}}$ letter of the alphabet. Code part: 18
• O is the $\text{15}^{\text{th}}$ letter of the alphabet. Code part: 15
• Y is the $\text{25}^{\text{th}}$ letter of the alphabet. Code part: 25

To get the final code for DESTROY, we concatenate these code parts in order:

4 + 5 + 19 + 20 + 18 + 15 + 25 = 451920181525.

Matching the Calculated Code with Options

Let's compare the code we calculated for DESTROY (451920181525) with the provided options:

• Option 1: 451920181525
• Option 2: 45192018125
• Option 3: 451920181425
• Option 4: 451920191525

Our calculated code 451920181525 exactly matches Option 1.

Therefore, the code for 'DESTROY' in this language is 451920181525.