Decoding the Word Puzzle: DELTOID to LOTION

This question involves a coding or cipher logic where a word is represented by a sequence of numbers. We need to decipher the pattern used for the word 'DELTOID' and apply it to find the code for the word 'LOTION'.

Step 1: Analyzing the Given Code

The problem states that the word 'DELTOID' is written as the number '$3152893$'. Let's break this down by mapping each letter of 'DELTOID' to its corresponding digit in the code:

• D -> 3
• E -> 1
• L -> 5
• T -> 2
• O -> 8
• I -> 9
• D -> 3

We observe that the mapping is consistent, with the letter 'D' appearing twice and mapping to the digit '3' both times. This suggests a direct substitution based on the letters present in the word 'DELTOID'.

Step 2: Establishing the Letter-to-Digit Mapping

From the analysis in Step 1, we can establish the following known mappings:

Step 3: Applying the Mapping to LOTION

Now, we need to find the code for the word 'LOTION' using the mappings we've established. Let's apply the code to each letter of 'LOTION':

• L -> 5
• O -> 8
• T -> 2
• I -> 9
• O -> 8
• N -> ?

Based on the known mappings, the code for 'LOTION' starts with '$58298$'. We need to determine the digit corresponding to the letter 'N'.

Step 4: Deducing the Code for 'N'

The letter 'N' does not appear in the word 'DELTOID', so its code is not directly provided by the example. However, we can use the given options to deduce the code for 'N'. The options are:

$582986$

$582981$

$198396$

$198392$

Options 3 and 4 start with '$198...$', which does not match the '$58298...$' prefix derived from the known mappings for L, O, T, and I. Therefore, we can eliminate options 3 and 4.

We are left with options 1 ($582986$) and 2 ($582981$). The difference lies in the last digit, which corresponds to 'N'.

Looking back at the established mapping, the digit '1' is already assigned to the letter 'E'. In this type of coding puzzle, it's common for different letters to map to different digits unless stated otherwise. Since 'E' is already '1', it's less likely that 'N' would also be '1'.

Therefore, the most logical conclusion is that 'N' maps to the digit '6'.

Step 5: Final Code Determination

Using the deduced mapping where N -> 6, we can construct the complete code for 'LOTION':

• L -> 5
• O -> 8
• T -> 2
• I -> 9
• O -> 8
• N -> 6

Combining these digits gives the final code: '$582986$'.